#2849 closed defect (fixed)
[with patch, positive review] Bug in elliptic curve cardinality for j=0 in char. 3
Reported by: | cremona | Owned by: | cremona |
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Priority: | major | Milestone: | |
Component: | number theory | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
Dustin Moody reported
While working on some things, I found a bug in SAGE: sage:k.<a>=GF(3^5) sage:E=EllipticCurve(k,[-1,-1]) sage:E.trace_of_frobenius() 0 This isn't correct. It should be -27. I also discovered you can get around it. sage:E.cardinality_exhaustive() 271 sage:E.trace_of_frobenius() -27 Somehow, doing .cardinality_exhaustive() fixes the bug.
Attachments (2)
Change History (6)
Changed 12 years ago by
comment:1 Changed 12 years ago by
- Summary changed from Bug in elliptic curve cardinality for j=0 in char. 3 to [with patch, needs review -- quick!] Bug in elliptic curve cardinality for j=0 in char. 3
comment:2 follow-up: ↓ 4 Changed 12 years ago by
- Summary changed from [with patch, needs review -- quick!] Bug in elliptic curve cardinality for j=0 in char. 3 to [with patch, positive review] Bug in elliptic curve cardinality for j=0 in char. 3
Looks fine and it fixes the issue. I've added a mini-patch that puts in a doctest demonstrating the fixed status.
Apply both patches.
comment:3 Changed 12 years ago by
- Resolution set to fixed
- Status changed from new to closed
Merged trac2849.patch and trac2849_doctest.patch in Sage 3.0.alpha3
comment:4 in reply to: ↑ 2 Changed 12 years ago by
Replying to AlexGhitza:
Looks fine and it fixes the issue. I've added a mini-patch that puts in a doctest demonstrating the fixed status.
Thanks, Alex -- I should have done that but only remembered after uploading the patch.
Apply both patches.
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Here's the patch: A case where q=3 (mod 4) only worked for p>3 and was being used for p=3, odd degree. Should be a trivial review.
Note that I am in the middle of implementing vastly better support for the cases j=0 and j=1728, which are not so straightforward in characterisitcs 2 and 3 but I am getting there!