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Elliptic Curves over the Rational Field
New Features:
- A new implementation of SIntegralPoints is included, replacing
the flawed one that has been there for some years. In addition to
correctness, significant improvements in performance will be noticed.
There are a number of innovations in the method for reducing the bound.
The special case of IntegralPoints, which had already been mostly
rewritten and made reliable in Magma V2.14, has also benefited from
the current improvements. Ongoing work will be done to speed up several
key parts of the code, and included in forthcoming patch releases.
- The ability to compute the p-adic height of a point on
a curve over the rationals has been added. Similarly, the p-adic
regulator can now be used. These rely on the EisensteinTwo
function, which computes the relevant Eisenstein series.
Bug fixes:
- A bug whereby CasselsTatePairing was occasionally unable to find
local points has been fixed.
- A long standing bug in the rank computation has been fixed.
This bug would occasionally cause the upper bound on the rank to
be incorrectly reported as one or even two less than it should be.
It could arise when there were ``small'' two-coverings with hard
to find points, and ``large'' two-coverings with easy to find points.
Next: Elliptic Curves over Number
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