#16034: Remember points of infinite order on an elliptic curve when extending
the
base field
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Reporter: pbruin | Owner:
Type: | Status: new
enhancement | Milestone: sage-6.2
Priority: minor | Keywords: elliptic curve Mordell-Weil
Component: elliptic | group base extension
curves | Authors:
Merged in: | Report Upstream: N/A
Reviewers: | Branch:
Work issues: | Dependencies:
Commit: |
Stopgaps: |
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It would be useful if elliptic curves over number fields remembered known
points of infinite order when extending the base field:
{{{
sage: E = EllipticCurve([1,0,1,-1751,-31352])
sage: K.<d>=QuadraticField(5)
sage: E.gens()
[(52 : 111 : 1)]
sage: EK = E.base_extend(K)
sage: EK.gens()
[]
}}}
These remembered points can be used by `EK.gens()`, and more generally
`EK.simon_two_descent()`, via the `help` parameter of Simon's function
`bnfellrank()`.
--
Ticket URL: <http://trac.sagemath.org/ticket/16034>
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