#17869: prove_BSD for elliptic curve uses an incorrect lemma
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Reporter: wuthrich | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: elliptic curves | Resolution:
Keywords: BSD | Merged in:
Authors: Chris Wuthrich | Reviewers: Peter Bruin
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/wuthrich/ticket/17869 | 8b6a73af07a1c0829a09133a0af9fcef1b724eee
Dependencies: | Stopgaps:
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Comment (by pbruin):
Looking at Theorem 1 in the preprint, it seems that the checks in the
cases ''p'' = 3 and ''p'' = 5 are stricter than necessary. For example,
let ''E'' be the (Γ,,0,,(''N'')-optimal) elliptic curve with Cremona label
198b1 (LMFDB label 198.e3). Then ''E'' admits a 3-isogeny with kernel
''μ'',,3,, and no other 3-isogenies. Theorem 1 implies that the H^1^ is
trivial, but the code as implemented in this ticket does not detect this
since it keeps `crit_lw = False` unless the 3-isogenous curve does not
have any points of order 3 either. Does this mean that the criterion in
the code can be relaxed?
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Ticket URL: <http://trac.sagemath.org/ticket/17869#comment:9>
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