| [1] |
Amod Agashe, Kenneth Ribet, and William A. Stein.
The Manin constant.
Pure Appl. Math. Q., 2(2):617–636, 2006. |
| [2] |
Amod Agashe and William Stein.
Visibility of Shafarevich-Tate groups of abelian varieties.
J. Number Theory, 97(1):171–185, 2002. |
| [3] |
Amod Agashe and William Stein.
Visible evidence for the Birch and Swinnerton-Dyer conjecture
for modular abelian varieties of analytic rank zero.
Math. Comp., 74(249):455–484 (electronic), 2005. |
| [4] |
Scott Ahlgren and Matthew Papanikolas.
Higher Weierstrass points on X0(p).
Trans. Amer. Math. Soc., 355(4):1521–1535 (electronic), 2003. |
| [5] |
Avner Ash, Darrin Doud, and David Pollack.
Galois representations with conjectural connections to arithmetic
cohomology.
Duke Math. J., 112(3):521–579, 2002. |
| [6] |
Matthew H. Baker, Enrique González-Jiménez, Josep González, and
Bjorn Poonen.
Finiteness results for modular curves of genus at least 2.
Amer. J. Math., 127(6):1325–1387, 2005. |
| [7] |
Arthur Baragar and Ronald van Luijk.
K3 surfaces with Picard number three and canonical vector
heights.
Math. Comp., 76(259):1493–1498 (electronic), 2007. |
| [8] |
Mark Bauer, Edlyn Teske, and Annegret Weng.
Point counting on Picard curves in large characteristic.
Math. Comp., 74(252):1983–2005 (electronic), 2005. |
| [9] |
Tobias Berger and Krzysztof Klosin.
A deformation problem for Galois representations over imaginary
quadratic fields.
J. Inst. Math. Jussieu, 8(4):669–692, 2009. |
| [10] |
Amnon Besser and Rob De Jeu.
li(p)-service? an algorithm for computing p-adic
polyalgorithms.
Math. Comp., 77(262):1105–1134, 2008. |
| [11] |
Peter Birkner.
Efficient Arithmetic on Low-genus Curves.
Ph D thesis, Technische Universiteit Eindhoven, 2009. |
| [12] |
Nigel Boston and Rafe Jones.
Arboreal Galois representations.
Geom. Dedicata, 124:27–35, 2007. |
| [13] |
M. J. Bright, N. Bruin, E. V. Flynn, and A. Logan.
The Brauer-Manin obstruction and Sh[2].
LMS J. Comput. Math., 10:354–377 (electronic), 2007. |
| [14] |
David Brown.
The Chabauty-Coleman bound at a prime of bad reduction.
arXiv:0803.0973v2 [math.NT], 10 pages, 2008. |
| [15] |
Ezra Brown and Bruce T. Myers.
Elliptic curves from Mordell to Diophantus and back.
Amer. Math. Monthly, 109(7):639–649, 2002. |
| [16] |
N. Bruin and E. V. Flynn.
n-covers of hyperelliptic curves.
Math. Proc. Cambridge Philos. Soc., 134(3):397–405, 2003. |
| [17] |
Nils Bruin.
Visualising Sha[2] in abelian surfaces.
Math. Comp., 73(247):1459–1476 (electronic), 2004. |
| [18] |
Nils Bruin.
The arithmetic of Prym varieties in genus 3.
Compos. Math., 144(2):317–338, 2008. |
| [19] |
Nils Bruin and Noam D. Elkies.
Trinomials ax7 + bx + c and ax8 + bx + c with Galois groups of
order 168 and 8·168.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 172–188. Springer, Berlin, 2002. |
| [20] |
Nils Bruin and E. Victor Flynn.
Towers of 2-covers of hyperelliptic curves.
Trans. Amer. Math. Soc., 357(11):4329–4347 (electronic), 2005. |
| [21] |
Nils Bruin and Michael Stoll.
Deciding existence of rational points on curves: an experiment.
Experiment. Math., 17(2):181–189, 2008. |
| [22] |
Nils Bruin and Michael Stoll.
Two-cover descent on hyperelliptic curves.
arXiv:0803.2052v1 [math.NT], 19 pages, 2008. |
| [23] |
Yann Bugeaud, Maurice Mignotte, Samir Siksek, Michael Stoll, and Szabolcs
Tengely.
Integral points on hyperelliptic curves.
Algebra Number Theory, 2(8):859–885, 2008. |
| [24] |
Kevin Buzzard and L. J. P. Kilford.
The 2-adic eigencurve at the boundary of weight space.
Compos. Math., 141(3):605–619, 2005. |
| [25] |
Robert Carls.
Theta null points of 2-adic canonical lifts.
arXiv:math.NT/0509092, 18 pages, 2005. |
| [26] |
Robert Carls and David Lubicz.
A p-adic quasi-quadratic time point counting algorithm.
Int. Math. Res. Not. IMRN, (4):698–735, 2009. |
| [27] |
Antoine Chambert-Loir.
Compter (rapidement) le nombre de solutions d'equations dans les
corps finis.
arXiv:math.NT/0611584, 46 pages, 2006. |
| [28] |
Denis Charles and Kristin Lauter.
Computing modular polynomials.
LMS J. Comput. Math., 8:195–204 (electronic), 2005. |
| [29] |
Denis Xavier Charles.
Complex multiplication tests for elliptic curves.
arXiv:math.NT/0409501 v1, 13 pages, 2004. |
| [30] |
Imin Chen.
On the equation s² + y2p = α³.
Math. Comp., 77(262):1223–1227, 2008. |
| [31] |
Imin Chen and Chris Cummins.
Elliptic curves with nonsplit mod 11 representations.
Math. Comp., 73(246):869–880 (electronic), 2004. |
| [32] |
Robert F. Coleman and William A. Stein.
Approximation of eigenforms of infinite slope by eigenforms of finite
slope.
In Geometric Aspects of Dwork Theory. Vol. I, II, pages
437–449. Walter de Gruyter GmbH & Co. KG, Berlin, 2004. |
| [33] |
B. Conrad, K. Conrad, and H. Helfgott.
Root numbers and ranks in positive characteristic.
Adv. Math., 198(2):684–731, 2005. |
| [34] |
Brian Conrad, Bas Edixhoven, and William Stein.
J1(p) has connected fibers.
Doc. Math., 8:331–408 (electronic), 2003. |
| [35] |
Caterina Consani and Jasper Scholten.
Arithmetic on a quintic threefold.
Internat. J. Math., 12(8):943–972, 2001. |
| [36] |
Patrick Kenneth Corn.
Del Pezzo Surfaces and the Brauer-Manin Obstruction.
PhD Thesis, University of California, Berkley, 1998. |
| [37] |
J. E. Cremona.
Algorithms for Modular Elliptic Curves.
Cambridge University Press, Cambridge, second edition, 1997. |
| [38] |
J. E. Cremona, T. A. Fisher, C. O'Neil, D. Simon, and M. Stoll.
Explicit n-descent on elliptic curves. I. Algebra.
J. Reine Angew. Math., 615:121–155, 2008. |
| [39] |
J. E. Cremona and M. P. Lingham.
Finding all elliptic curves with good reduction outside a given set
of primes.
Experiment. Math., 16(3):303–312, 2007. |
| [40] |
J. E. Cremona, M. Prickett, and Samir Siksek.
Height difference bounds for elliptic curves over number fields.
J. Number Theory, 116(1):42–68, 2006. |
| [41] |
John Cremona.
The elliptic curve database for conductors to 130000.
In Algorithmic number theory, volume 4076 of Lecture Notes
in Comput. Sci., pages 11–29. Springer, Berlin, 2006. |
| [42] |
John Cremona, Tom Fisher, Cathy O'Neil, Denis Simon, and Michael Stoll.
Explicit n-descent on elliptic curves II: Geometry.
arXiv:math.NT/0611606, 24 pages, 2006. |
| [43] |
John E. Cremona.
A solution for note 84.35.
The Mathematical Gazette, 86(505):66–68, 2002. |
| [44] |
John Cullinan.
A computational approach to the 2-torsion structure of abelian
threefolds.
Math. Comp., 78(267):1825–1836, 2009. |
| [45] |
C. J. Cummins and S. Pauli.
Congruence subgroups of PSL(2, Z) of genus less than or
equal to 24.
Experiment. Math., 12(2):243–255, 2003. |
| [46] |
Samit Dasgupta.
Computations of elliptic units for real quadratic fields.
Canad. J. Math., 59(3):553–574, 2007. |
| [47] |
Chantal David and Tom Weston.
Local torsion on elliptic curves and the deformation theory of
Galois representations.
Math. Res. Lett., 15(3):599–611, 2008. |
| [48] |
Lassina Dembélé.
A non-solvable galois extension of q ramified at 2 only.
C. R., Math., Acad. Sci. Paris, 347(3-4), 2009. |
| [49] |
Jan Denef and Frederik Vercauteren.
An extension of Kedlaya's algorithm to Artin-Schreier curves in
characteristic 2.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 308–323. Springer, Berlin, 2002. |
| [50] |
Xavier Charles Denis.
Complex multiplication tests for elliptic curves.
Preprint, 13 pages, 2004. |
| [51] |
Claus Diem and Emmanuel Thomé.
Index calculus in class groups of non-hyperelliptic curves of genus
three.
J. Cryptology, 21(4):593–611, 2008. |
| [52] |
T. Dokchitser and V. Dokchitser.
Computations in non-commutative Iwasawa theory.
Proc. Lond. Math. Soc. (3), 94(1):211–272, 2007. |
| [53] |
Tim Dokchitser and Vladimir Dokchitser.
Root numbers of elliptic curves in residue characteristic 2.
Bull. Lond. Math. Soc., 40(3):516–524, 2008. |
| [54] |
Darrin Doud.
A procedure to calculate torsion of elliptic curves over Q.
Manuscripta Math., 95(4):463–469, 1998. |
| [55] |
Andrej Dujella.
On Mordell-Weil groups of elliptic curves induced by
Diophantine triples.
Glas. Mat. Ser. III, 42(62)(1):3–18, 2007. |
| [56] |
S. Duquesne.
Rational points on hyperelliptic curves and an explicit Weierstrass
preparation theorem.
Manuscripta Math., 108(2):191–204, 2002. |
| [57] |
Sylvain Duquesne.
Points rationnels et méthode de Chabauty elliptique.
J. Théor. Nombres Bordeaux, 15(1):99–113, 2003. |
| [58] |
Sylvain Duquesne.
Elliptic curves associated with simplest quartic fields.
J. Théor. Nombres Bordeaux, 19(1):81–100, 2007. |
| [59] |
Sylvain Duquesne.
Montgomery ladder for all genus 2 curves in characteristic 2.
In Arithmetic of Finite Fields, volume 5130 of Lecture
Notes in Computer Science, pages 174–188. Springer, 2008. |
| [60] |
Bas Edixhoven.
On the computation of the coefficients of a modular form.
In Algorithmic number theory, volume 4076 of Lecture Notes
in Comput. Sci., pages 30–39. Springer, Berlin, 2006. |
| [61] |
Kirsten Eisentraeger, Dimitar Jetchev, and Kristin Lauter.
On the computation of the Cassels pairing for certain Kolyvagin
classes in the Shafarevich-Tate group.
5209:113–125, 2008. |
| [62] |
Kirsten Eisenträger and Kristin Lauter.
A CRT algorithm for constructing genus 2 curves over finite fields.
arXiv:math.NT/0405305v2, 16 pages, 2007. |
| [63] |
Noam D. Elkies.
Three lectures on elliptic surfaces and curves of high rank.
arXiv:0709.2908v1, 14 pages, 2007. |
| [64] |
Noam D. Elkies.
Shimura curve computations via K3 surfaces of Neron-Severi rank
at least 19.
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 196–211. Springer, 2008. |
| [65] |
Noam D. Elkies and Mark Watkins.
Elliptic curves of large rank and small conductor.
In Algorithmic Number Theory, volume 3076 of Lecture
Notes in Comput. Sci., pages 42–56. Springer, Berlin, 2004. |
| [66] |
Arsen Elkin.
Hyperelliptic Jacobians with real multiplication.
J. Number Theory, 117(1):53–86, 2006. |
| [67] |
Andreas-Stephan Elsenhans and Jörg Jahnel.
K3 surfaces of Picard rank one and degree two.
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 212–225. Springer, 2008. |
| [68] |
G. Everest and T. Ward.
The canonical height of an algebraic point on an elliptic curve.
New York J. Math., 6:331–342 (electronic), 2000. |
| [69] |
Graham Everest, Patrick Ingram, Valéry Mahé, and Shaun Stevens.
The uniform primality conjecture for elliptic curves.
Acta Arith., 134(2):157–181, 2008. |
| [70] |
Graham Everest, Patrick Ingram, and Shaun Stevens.
Primitive divisors on twists of Fermat's cubic.
LMS J. Comput. Math., 12:54–81, 2009. |
| [71] |
Graham Everest and Valery Mahe.
A generalization of Siegel's theorem and Hall's conjecture.
Exp. Math., 18(1):1–10, 2009. |
| [72] |
Xander Faber and Benjamin Hutz.
On the number of rational iterated pre-images of the origin under
quadratic dynamical systems.
arXiv:0810.1715, 18 pages, 2008. |
| [73] |
Reza Rezaeian Farashahi and Ruud Pellikaan.
The quadratic extension extractor for (hyper)elliptic curves in odd
characteristic.
In Arithmetic of finite fields, volume 4547 of Lecture
Notes in Comput. Sci., pages 219–236. Springer, Berlin, 2007. |
| [74] |
Julio Fernández, Josep González, and Joan-C. Lario.
Plane quartic twists of X(5, 3).
Canad. Math. Bull., 50(2):196–205, 2007. |
| [75] |
Luís R. A. Finotti.
Degrees of the elliptic Teichmüller lift.
J. Number Theory, 95(2):123–141, 2002. |
| [76] |
Luís R. A. Finotti.
Minimal degree liftings of hyperelliptic curves.
J. Math. Sci. Univ. Tokyo, 11(1):1–47, 2004. |
| [77] |
Luís R. A. Finotti.
Minimal degree liftings in characteristic 2.
J. Pure Appl. Algebra, 207(3):631–673, 2006. |
| [78] |
Tom Fisher.
The Hessian of a genus one curve.
arXiv:math.NT/0610403, 28 pages, 2006. |
| [79] |
Tom Fisher.
Testing equivalence of ternary cubics.
In Algorithmic Number Theory (Berlin, 2006), volume 4076 of
Lecture Notes in Comput. Sci., pages 333–345. Springer, Berlin, 2006. |
| [80] |
Tom Fisher.
A new approach to minimising binary quartics and ternary cubics.
Math. Res. Lett., 14(4):597–613, 2007. |
| [81] |
Tom Fisher.
The invariants of a genus one curve.
Proc. Lond. Math. Soc. (3), 97(3):753–782, 2008. |
| [82] |
E. V. Flynn.
The Hasse principle and the Brauer-Manin obstruction for
curves.
Manuscripta Math., 115(4):437–466, 2004. |
| [83] |
E. V. Flynn and C. Grattoni.
Descent via isogeny on elliptic curves with large rational torsion
subgroups.
J. Symbolic Comput., 43(4):293–303, 2008. |
| [84] |
E. V. Flynn and J. Wunderle.
Cycles of covers.
Monatsh. Math., Online first:16, 2008. |
| [85] |
David Freeman, Peter Stevenhagen, and Marco Streng.
Abelian varieties with prescribed embedding degree.
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 60–73. Springer, 2008. |
| [86] |
S. D. Galbraith, J. F. McKee, and P. C. Valença.
Ordinary abelian varieties having small embedding degree.
Finite Fields Appl., 13(4):800–814, 2007. |
| [87] |
Steven D. Galbraith.
Weil descent of Jacobians.
Discrete Appl. Math., 128(1):165–180, 2003. |
| [88] |
P. Gaudry and É. Schost.
Modular equations for hyperelliptic curves.
Math. Comp., 74(249):429–454 (electronic), 2005. |
| [89] |
Pierrick Gaudry.
Index calculus for abelian varieties and the elliptic curve discrete
logarithm problem.
Preprint, 13 pages, 2004. |
| [90] |
Pierrick Gaudry and Nicolas Gürel.
An extension of Kedlaya's point-counting algorithm to superelliptic
curves.
In Advances in Cryptology—Asiacrypt 2001 (Gold Coast),
volume 2248 of Lecture Notes in Comput. Sci., pages 480–494. Springer,
Berlin, 2001. |
| [91] |
Pierrick Gaudry and Robert Harley.
Counting points on hyperelliptic curves over finite fields.
In Algorithmic Number Theory (Leiden, 2000), volume 1838 of
Lecture Notes in Comput. Sci., pages 313–332. Springer, Berlin, 2000. |
| [92] |
Eknath Ghate, Enrique González-Jiménez, and Jordi Quer.
On the Brauer class of modular endomorphism algebras.
Int. Math. Res. Not., (12):701–723, 2005. |
| [93] |
Jean Gillibert.
Invariants de classes: exemples de non-annulation en dimension
supérieure.
Math. Ann., 338(2):475–495, 2007. |
| [94] |
Edray Goins.
Explicit descent via 4-isogeny on an elliptic curve.
arXiv:math.NT/0411215 v1, 20 pages, 2004. |
| [95] |
Josep González and Jordi Guàrdia.
Genus two curves with quaternionic multiplication and modular
Jacobian.
Math. Comp., 78(265):575–589, 2009. |
| [96] |
Josep González, Jordi Guàrdia, and Victor Rotger.
Abelian surfaces of GL2-type as Jacobians of curves.
Acta Arith., 116(3):263–287, 2005. |
| [97] |
Josep González and Victor Rotger.
Non-elliptic Shimura curves of genus one.
J. Math. Soc. Japan, 58(4):927–948, 2006. |
| [98] |
Enrique González-Jiménez, Josep González, and Jordi Guàrdia.
Computations on modular Jacobian surfaces.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 189–197. Springer, Berlin, 2002. |
| [99] |
Eyal Z. Goren and Kristin E. Lauter.
The distance between superspecial abelian varieties with real
multiplication.
J. Number Theory, 129(6):1562–1578, 2009. |
| [100] |
Matthew Greenberg.
Computing Heegner points arising from Shimura curve
parametrizations.
Preprint, 11 pages, 2006. |
| [101] |
Matthew Greenberg.
Heegner point computations via numerical p-adic integration.
In Algorithmic Number Theory, volume 4076 of Lecture
Notes in Computer Science, pages 361–376. Springer Berlin / Heidelberg,
2006. |
| [102] |
Matthew Greenberg.
Heegner Points and Rigid Analytic Modular Forms.
PhD Thesis, McGill University, 2006. |
| [103] |
Grigor Grigorov, Andrei Jorza, Stephan Patrikis, William A. Stein, and Corina
Tarnita-Patrascu.
Verification of the Birch and Swinnerton-Dyer conjecture for
specific elliptic curves.
Preprint, 26 pages. |
| [104] |
Jordi Guàrdia.
Jacobian Nullwerte, periods and symmetric equations for
hyperelliptic curves.
Ann. Inst. Fourier (Grenoble), 57(4):1253–1283, 2007. |
| [105] |
Brian Hansen.
Explicit computations supporting a generalization of Serre's
conjecture.
Master of Science thesis, Brigham Young University, 2005. |
| [106] |
Robin Hartshorne and Ronald van Luijk.
Non-Euclidean Pythagorean triples, a problem of Euler, and
rational points on K3 surfaces.
Math. Intelligencer, 30(4):4–10, 2008. |
| [107] |
Ki-ichiro Hashimoto, Katsuya Miyake, and Hiroaki Nakamura, editors.
Galois Theory and Modular Forms, volume 11 of Developments in Mathematics, Boston, MA, 2004. Kluwer Academic Publishers. |
| [108] |
Florian Hess.
Computing relations in divisor class groups of algebraic curves over
finite fields.
Preprint, 2003. |
| [109] |
Florian Hess.
A note on the Tate pairing of curves over finite fields.
Arch. Math. (Basel), 82(1):28–32, 2004. |
| [110] |
Laura Hitt.
Families of genus 2 curves with small embedding degree.
J. Math. Cryptol., 3(1):19–36, 2009. |
| [111] |
E. W. Howe and K. E. Lauter.
Improved upper bounds for the number of points on curves over finite
fields.
Ann. Inst. Fourier (Grenoble), 53(6):1677–1737, 2003. |
| [112] |
Everett W. Howe.
Infinite families of pairs of curves over Q with isomorphic
Jacobians.
J. London Math. Soc. (2), 72(2):327–350, 2005. |
| [113] |
Everett W. Howe.
Supersingular genus-2 curves over fields of characteristic 3.
In Computational arithmetic geometry, volume 463 of Contemp. Math., pages 49–69. Amer. Math. Soc., Providence, RI, 2008. |
| [114] |
Everett W. Howe, Kristin E. Lauter, and Jaap Top.
Pointless curves of genus three and four.
In Arithmetic, Geometry and Coding Theory (AGCT 2003),
volume 11 of Sémin. Congr., pages 125–141. Soc. Math. France,
Paris, 2005. |
| [115] |
Everett W. Howe and Hui June Zhu.
On the existence of absolutely simple abelian varieties of a given
dimension over an arbitrary field.
J. Number Theory, 92(1):139–163, 2002. |
| [116] |
Hendrik Hubrechts.
Point counting in families of hyperelliptic curves.
Found. Comput. Math., 8(1):137–169, 2008. |
| [117] |
Hendrik Hubrechts.
Quasi-quadratic elliptic curve point counting using rigid cohomology.
J. Symb. Comput., 44(9):1255–1267, 2009. |
| [118] |
Klaus Hulek and Helena Verrill.
On modularity of rigid and nonrigid Calabi-Yau varieties
associated to the root lattice A4.
Nagoya Math. J., 179:103–146, 2005. |
| [119] |
Klaus Hulek and Helena A. Verrill.
On the motive of Kummer varieties associated to Γ1(7)—
Supplement to the paper: ``The modularity of certain non-rigid
Calabi-Yau threefolds'' by R. Livné and N. Yui.
J. Math. Kyoto Univ., 45(4):667–681, 2005. |
| [120] |
Patrick Ingram.
Multiples of integral points on elliptic curves.
Journal of Number Theory, 129(1):182 – 208, 2009. |
| [121] |
Farzali A. Izadi and V. Kumar Murty.
Counting points on an abelian variety over a finite field.
In Progress in Cryptology—Indocrypt 2003, volume 2904 of
Lecture Notes in Comput. Sci., pages 323–333. Springer, Berlin, 2003. |
| [122] |
Dimitar Jetchev, Kristin Lauter, and William Stein.
Explicit Heegner points: Kolyvagin's conjecture and non-trivial
elements in the Shafarevich-Tate group.
Journal of Number Theory, 129(2):284 – 302, 2009. |
| [123] |
Dimitar P. Jetchev and William A. Stein.
Visibility of the Shafarevich-Tate group at higher level.
Doc. Math., 12:673–696, 2007. |
| [124] |
Jorge Jimenez-Urroz and Tonghai Yang.
Heegner zeros of theta functions.
Trans. Amer. Math. Soc., 355(10):4137–4149 (electronic), 2003. |
| [125] |
David Joyner and Amy Ksir.
Modular representations on some Riemann-Roch spaces of modular
curves X(N).
In Computational Aspects of Algebraic Curves, volume 13
of Lecture Notes Ser. Comput., pages 163–205. World Sci. Publ.,
Hackensack, NJ, 2005. |
| [126] |
Koray Karabina and Edlyn Teske.
On prime-order elliptic curves with embedding degrees k=3,4, and 6.
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 102–117. Springer, 2008. |
| [127] |
L. J. P. Kilford.
Some non-Gorenstein Hecke algebras attached to spaces of modular
forms.
J. Number Theory, 97(1):157–164, 2002. |
| [128] |
L. J. P. Kilford.
Slopes of 2-adic overconvergent modular forms with small level.
Math. Res. Lett., 11(5-6):723–739, 2004. |
| [129] |
L. J. P. Kilford.
On a p-adic extension of the Jacquet-Langlands correspondence
to weight 1.
arXiv:0809.1048v1 [math.NT], 17 pages, 2008. |
| [130] |
David R. Kohel.
Hecke module structure of quaternions.
In Class Field Theory—Its Centenary and Prospect
(Tokyo, 1998), volume 30 of Adv. Stud. Pure Math., pages 177–195.
Math. Soc. Japan, Tokyo, 2001. |
| [131] |
David R. Kohel.
The AGM-X0(N) Heegner point lifting algorithm and elliptic
curve point counting.
In Advances in Cryptology—Asiacrypt 2003, volume 2894 of
Lecture Notes in Comput. Sci., pages 124–136. Springer, Berlin, 2003. |
| [132] |
David R. Kohel and William A. Stein.
Component groups of quotients of J0(N).
In Algorithmic Number Theory (Leiden, 2000), volume 1838 of
Lecture Notes in Comput. Sci., pages 405–412. Springer, Berlin, 2000. |
| [133] |
David R. Kohel and Helena A. Verrill.
Fundamental domains for Shimura curves.
J. Théor. Nombres Bordeaux, 15(1):205–222, 2003. |
| [134] |
Kenji Koike and Annegret Weng.
Construction of CM Picard curves.
Math. Comp., 74(249):499–518 (electronic), 2005. |
| [135] |
Elisavet Konstantinou and Kontogeorgis Aristides.
Computing polynomials of the Ramanujan tn class
invariants.
Canad. Math. Bull., To appear, 12 pages, 2007. |
| [136] |
Aristides Kontogeorgis and Victor Rotger.
On the non-existence of exceptional automorphisms on Shimura
curves.
Bull. Lond. Math. Soc., 40(3):363–374, 2008. |
| [137] |
Andrew Kresch and Yuri Tschinkel.
Integral points on punctured abelian surfaces.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 198–204. Springer, Berlin, 2002. |
| [138] |
L. Kulesz, G. Matera, and É. Schost.
Uniform bounds on the number of rational points of a family of curves
of genus 2.
J. Number Theory, 108(2):241–267, 2004. |
| [139] |
Dominic Lanphier.
The trace of special values of modular L-functions.
Preprint, 18 pages. |
| [140] |
Alan G. B. Lauder.
Ranks of elliptic curves over function fields.
LMS J. Comput. Math., 11:172–212, 2008. |
| [141] |
F. Leprévost, M. Pohst, and A. Schöpp.
Rational torsion of J0(N) for hyperelliptic modular curves and
families of Jacobians of genus 2 and genus 3 curves with a rational point
of order 5, 7 or 10.
Abh. Math. Sem. Univ. Hamburg, 74:193–203, 2004. |
| [142] |
Franck Leprévost, Michael Pohst, and Andreas Schöpp.
Familles de polynômes liées aux courbes modulaires X(l)
unicursales et points rationnels non-triviaux de courbes elliptiques
quotient.
Acta Arith., 110(4):401–410, 2003. |
| [143] |
Reynald Lercier and David Lubicz.
A quasi-quadratic time algorithm for hyperelliptic curve point
counting.
The Ramanujan Journal, 12(3):399–423, 2006. |
| [144] |
Reynald Lercier and Thomas Sirvent.
On Elkies subgroups of l-torsion points in elliptic curves
defined over a finite field.
J. Théor. Nombres Bordeaux, 20(3):783–797, 2008. |
| [145] |
David Loeffler.
Explicit calculations of automorphic forms for definite unitary
groups.
LMS J. Comput. Math., 11:326–342, 2008. |
| [146] |
Adam Logan and Ronald van Luijk.
Nontrivial elements of Sha explained through K3 surfaces.
Math. Comp., 78(265):441–483, 2009. |
| [147] |
Ling Long and Chris Kurth.
On modular forms for some noncongruence subgroups of SL2Z)
II.
arXiv:0809.0020v1 [math.NT], 13 pages, 2008. |
| [148] |
Dino Lorenzini and Thomas J. Tucker.
Thue equations and the method of Coleman-Chabauty.
arXiv:math.NT/0005186, 30 pages, 2000. |
| [149] |
Kazuo Matsuno.
Construction of elliptic curves with large Iwasawa
λ-invariants and large Tate-Shafarevich groups.
Manuscripta Math., 122(3):289–304, 2007. |
| [150] |
Kazuto Matsuo, Jinhui Chao, and Shigeo Tsujii.
An improved baby step giant step algorithm for point counting of
hyperelliptic curves over finite fields.
In Algorithmic Number Theory (Sydney, 2002), volume 2369 of
Lecture Notes in Comput. Sci., pages 461–474. Springer, Berlin, 2002. |
| [151] |
J. Miret, R. Moreno, A. Rio, and M. Valls.
Computing the l-power torsion of an elliptic curve over a finite
field.
Math. Comp., 78(267):1767–1786, 2009. |
| [152] |
J. Miret, R. Moreno, D. Sadornil, J. Tena, and M. Valls.
Computing the height of volcanoes of l-isogenies of elliptic
curves over finite fields.
Appl. Math. Comput., 196(1):67–76, 2008. |
| [153] |
Annika Niehage.
Quantum Goppa Codes over Hypereliptic Curves.
Diplomarbeit, Universität Mannheim, 2004. |
| [154] |
Mihran Papikian.
On the variation of Tate-Shafarevich groups of elliptic curves
over hyperelliptic curves.
J. Number Theory, 115(2):249–283, 2005. |
| [155] |
Bernadette Perrin-Riou.
Arithmétique des courbes elliptiques à réduction
supersingulière en p.
Experiment. Math., 12(2):155–186, 2003. |
| [156] |
Bjorn Poonen.
Computational aspects of curves of genus at least 2.
In Algorithmic Number Theory (Talence, 1996), volume 1122
of Lecture Notes in Comput. Sci., pages 283–306. Springer, Berlin,
1996. |
| [157] |
Bjorn Poonen, Edward F. Schaefer, and Michael Stoll.
Twists of X(7) and primitive solutions to x² + y³ = z7.
Duke Math. J., 137(1):103–158, 2007. |
| [158] |
Lisa Marie Redekop.
Torsion Points of Low Order on Elliptic Curves and
Drinfeld Modules.
PhD thesis, 2002. |
| [159] |
Guillaume Ricotta and Thomas Vidick.
Hauteur asymptotique des points de Heegner.
Canad. J. Math., 60(6):1406–1436, 2008. |
| [160] |
Christophe Ritzenthaler.
Automorphismes des courbes modulaires X(n) en caractéristique
p.
Manuscripta Math., 109(1):49–62, 2002. |
| [161] |
Christophe Ritzenthaler.
Point counting on genus 3 non hyperelliptic curves.
In Algorithmic Number Theory, volume 3076 of Lecture
Notes in Comput. Sci., pages 379–394. Springer, Berlin, 2004. |
| [162] |
David Savitt.
The maximum number of points on a curve of genus 4 over F8 is
25.
Canad. J. Math., 55(2):331–352, 2003. |
| [163] |
Edward F. Schaefer and Michael Stoll.
How to do a p-descent on an elliptic curve.
Trans. Amer. Math. Soc., 356(3):1209–1231 (electronic), 2004. |
| [164] |
Jasper Scholten.
Weil restriction of an elliptic curve over a quadratic extension.
Preprint, 6 pages, 2004. |
| [165] |
Andreas M. Schöpp.
Über Torsionspunkte elliptischer und hyperelliptischer
Kurven nebst Anwendungen.
PhD thesis, Technische Universitaet Berlin,, April 2005. |
| [166] |
Samir Siksek.
On standardized models of isogenous elliptic curves.
Math. Comp., 74(250):949–951 (electronic), 2005. |
| [167] |
Samir Siksek and John E. Cremona.
On the Diophantine equation x² + 7 = ym.
Acta Arith., 109(2):143–149, 2003. |
| [168] |
Benjamin Smith.
Isogenies and the discrete logarithm problem in Jacobians of genus
3 hyperelliptic curves.
In Advances in Cryptology, Eurocrypt 2008, volume 4965 of Lecture Notes in Computer Science, pages 163–180. Springer
Berlin/Heidelberg, 2008. |
| [169] |
Sebastian Karl Michael Stamminger.
Explicit 8-Descent on Elliptic Curves.
PhD thesis, International University Bremen, 2005. |
| [170] |
William Stein.
Studying the Birch and Swinnerton-Dyer conjecture for modular
abelian varieties using Magma.
In Discovering Mathematics with Magma, volume 19 of Algorithms Comput. Math., pages 93–116. Springer, Berlin, 2006. |
| [171] |
William A. Stein.
There are genus one curves over Q of every odd index.
J. Reine Angew. Math., 547:139–147, 2002. |
| [172] |
William A. Stein.
Shafarevich-Tate groups of nonsquare order.
In Modular curves and abelian varieties, volume 224 of Progr. Math., pages 277–289. Birkhäuser, Basel, 2004. |
| [173] |
William A. Stein.
Visibility of Mordell-Weil groups.
Doc. Math., 12:587–606, 2007. |
| [174] |
Michael Stoll.
Implementing 2-descent for Jacobians of hyperelliptic curves.
Acta Arith., 98(3):245–277, 2001. |
| [175] |
Michael Stoll.
On the height constant for curves of genus two. II.
Acta Arith., 104(2):165–182, 2002. |
| [176] |
Michael Stoll.
Rational 6-cycles under iteration of quadratic polynomials.
LMS J. Comput. Math., 11:367–380, 2008. |
| [177] |
Thotsaphon Thongjunthug.
Computing a lower bound for the canonical height on elliptic curves
over totally real number fields.
In Algorithmic Number Theory, volume 5011 of Lecture Notes
in Computer Science, pages 139–152. Springer, 2008. |
| [178] |
Hans-Christian Graf v. Bothmer.
Finite field experiments (with an appendix by Stefan Wiedmann).
In Higher-Dimensional Geometry over Finite Fields, volume 16 of
NATO Science for Peace and Security Series, D: Information and
Communication Security, pages 1–62. 2008. |
| [179] |
Marie-France Vignéras.
p-adic integral structures of some representations of GL(2,
F).
Preprint, 23 pages, 2005. |
| [180] |
Bogdan G. Vioreanu.
Mordell-Weil problem for cubic surfaces, numerical evidence.
arXiv:0802.0742v1 [math.AG], 22 pages, 2008. |
| [181] |
Mark Watkins.
A note on integral points on elliptic curves.
J. Théor. Nombres Bordeaux, 18(3):707–720, 2006. |
| [182] |
Mark Watkins.
Some remarks on Heegner point computations.
arXiv:math.NT/0506325, 14 pages, 2006. |
| [183] |
Mark Watkins.
Some heuristics about elliptic curves.
Experiment. Math., 17(1):105–125, 2008. |
| [184] |
Rolf Stefan Wilke.
On rational embeddings of curves in the second Garcia-Stichtenoth
tower.
Finite Fields Appl., 14(2):494–504, 2008. |
| [185] |
Christian Wuthrich.
The fine Tate-Shafarevich group.
Math. Proc. Cambridge Philos. Soc., 142(1):1–12, 2007. |
| [186] |
Chaoping Xing.
Applications of algebraic curves to constructions of sequences.
In Cryptography and Computational Number Theory
(Singapore, 1999), volume 20 of Progr. Comput. Sci. Appl. Logic, pages
137–146. Birkhäuser, Basel, 2001. |
| [187] |
Chaoping Xing and Sze Ling Yeo.
Construction of global function fields from linear codes and vice
versa.
Trans. Amer. Math. Soc., 361(3):1333–1349, 2008. |
| [188] |
Huilin Zhu and Jianhua Chen.
Integral points on a class of elliptic curve.
Wuhan Univ. J. Nat. Sci., 11(3):477–480, 2006. |
