#9384 closed enhancement (fixed)
descend_to method for elliptic curves
Reported by: | ebeyerstedt | Owned by: | cremona |
---|---|---|---|
Priority: | minor | Milestone: | sage-4.5.2 |
Component: | elliptic curves | Keywords: | descend, subfield, isomorphic, elliptic curve |
Cc: | adeines, cremona, jeremywest | Merged in: | sage-4.5.2.alpha1 |
Authors: | Erin Beyerstedt, Jeremy West | Reviewers: | Aly Deines |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Given a subfield K and an elliptic curve E defined over a field L, this function determines whether there exists an elliptic curve over K which is isomorphic over L to E. If one exists, it finds it.
Attachments (2)
Change History (16)
comment:1 Changed 12 years ago by
- Status changed from new to needs_review
comment:2 Changed 12 years ago by
Note: This function does not yet work when j = 0, 1728.
Changed 12 years ago by
comment:3 Changed 12 years ago by
The update handles the cases for j=0,1728.
comment:4 Changed 12 years ago by
- Cc adeines added
comment:5 Changed 12 years ago by
- Cc cremona added
comment:6 Changed 12 years ago by
- Cc jeremywest added
- Status changed from needs_review to needs_work
The code for handling j=0,1728 needs to be cleaned up a little. Also, this function currently does not properly handle the following case
F.<b> = QuadraticField?(23) K.<a> = F.extension(x^{3+5) E = EllipticCurve?(j = 1728*b).change_ring(K) E.descend_to(F) }
It returns none when it should descend to the subfield F.
comment:7 Changed 12 years ago by
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]
comment:8 Changed 12 years ago by
- Status changed from needs_work to needs_review
This new patch should work in general. It uses the newly implemented preimage function for number field homomorphisms. Be sure to apply the patch from #9403 first.
comment:9 Changed 12 years ago by
- Status changed from needs_review to positive_review
comment:10 Changed 12 years ago by
- Merged in set to sage-4.5.2.alpha1
- Resolution set to fixed
- Status changed from positive_review to closed
comment:11 Changed 12 years ago by
- Milestone changed from sage-5.0 to sage-4.5.2
comment:12 Changed 12 years ago by
- Reviewers set to Alyson Deines
I'm entering a guess for the Reviewer(s) field. Please correct me if I'm wrong.
comment:13 Changed 12 years ago by
- Reviewers changed from Alyson Deines to Aly Deines
comment:14 Changed 8 years ago by
See follow-up ticket at #16456 where it is explained why the implementation here is deficient and needs fixing.
This has been implemented in the patch. Please review.