- Introduction
- Creation Functions
- Creation of an Elliptic Curve
- Creation Predicates
- Changing the Base Ring
- Alternative Models
- WeierstrassModel(E) : CrvEll -> CrvEll, Map, Map
- IntegralModel(E) : CrvEll -> CrvEll, Map, Map
- SimplifiedModel(E): CrvEll -> CrvEll, Map, Map
- MinimalModel(E) : CrvEll -> CrvEll, Map, Map
- MinimalModel(E, p) : CrvEll, RngIntElt -> CrvEll, Map, Map
- Predicates on Curve Models
- Twists of Elliptic Curves
- Operations on Curves
- Polynomials
- Subgroup Schemes
- The Formal Group
- Operations on Point Sets
- Morphisms
- Creation Functions
- Example CrvEll_Isogeny (H128E16)
- Isomorphism(E, F, [r, s, t, u]) : CrvEll, CrvEll, SeqEnum -> Map
- Isomorphism(E, F) : CrvEll, CrvEll -> Map
- Automorphism(E, [r, s, t, u]) : CrvEll, SeqEnum -> Map
- IsomorphismData(I) : Map -> [ RngElt ]
- Example CrvEll_Isomorphisms (H128E17)
- IsIsomorphism(I) : Map -> BoolElt, Map
- IsomorphismToIsogeny(I) : Map -> Map
- Example CrvEll_Isomorphism (H128E18)
- TranslationMap(E, P) : CrvEll, PtEll -> Map
- RationalMap(i, t) : Map, Map -> Map
- TwoIsogeny(P) : PtEll -> Map
- Example CrvEll_Map (H128E19)
- IsogenyFromKernel(G) : SchGrpEll -> CrvEll, Map
- IsogenyFromKernelFactored(G) : SchGrpEll -> CrvEll, Map
- IsogenyFromKernel(E, psi) : CrvEll, RngUPolElt -> CrvEll, Map
- IsogenyFromKernelFactored(E, psi) : SchGrpEll, RngUPolElt -> CrvEll, Map
- PushThroughIsogeny(I, v) : Map, RngUPolElt -> RngUPolElt
- DualIsogeny(phi) : Map -> Map
- Example CrvEll_DualIsogeny (H128E20)
- Predicates on Isogenies
- Structure Operations
- Endomorphisms
- Automorphisms
- Operations on Points
- Creation of Points
- Creation Predicates
- Access Operations
- Associated Structures
- Arithmetic
- Division Points
- Point Order
- Predicates on Points
- Weil Pairing
- WeilPairing(P, Q, n) : PtEll, PtEll, RngIntElt -> RngElt
- IsLinearlyIndependent(S, n) : [ PtEll ], RngIntElt -> BoolElt
- IsLinearlyIndependent(P, Q, n) : PtEll, PtEll, RngIntElt -> BoolElt
- Example CrvEll_WeilPairing (H128E27)
- Bibliography
V2.28, 13 July 2023