#9384: descend_to method for elliptic curves
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Reporter: ebeyerstedt | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.0
Component: elliptic curves | Keywords: descend, subfield,
isomorphic, elliptic curve
Author: Erin Beyerstedt, Jeremy West | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by cremona):
It looks to me as though the curve returned is (sometimes) a twist of the
original, rather than isomorphic -- but I have been flying all night so am
not reliable!
You can check if there is an embedding of K in self.base_ring() like this:
{{{
sage: X = polygen(QQ)
sage: K.<a> = NumberField(X^4 - X^3 + 2*X^2 + X + 1)
sage: QQ.embeddings(K)
[Ring Coercion morphism:
From: Rational Field
To: Number Field in a with defining polynomial x^4 - x^3 + 2*x^2 + x +
1]
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9384#comment:7>
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