Opened 3 years ago
Closed 3 years ago
#11346 closed defect (fixed)
major bug in the conductor function for elliptic curves over number fields
Reported by: | was | Owned by: | cremona |
---|---|---|---|
Priority: | critical | Milestone: | sage-4.7.1 |
Component: | elliptic curves | Keywords: | |
Cc: | Merged in: | sage-4.7.1.alpha2 | |
Authors: | William Stein | Reviewers: | Robert Bradshaw |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by was)
Joanna Gaski found a serious bug in the function for computing conductors of elliptic curves over number fields, when the input curve is not integral. Witness:
sage: K.<g> = NumberField(x^2 - x - 1) sage: E1 = EllipticCurve(K,[0,0,0,-1/48,-161/864]); E1 Elliptic Curve defined by y^2 = x^3 + (-1/48)*x + (-161/864) over Number Field in g with defining polynomial x^2 - x - 1 sage: factor(E1.conductor()) (Fractional ideal (3)) * (Fractional ideal (-2*g + 1)) sage: factor(E1.integral_model().conductor()) (Fractional ideal (2))^4 * (Fractional ideal (3)) * (Fractional ideal (-2*g + 1))
The bug is actually in the local_data() function, which computes the possible primes of bad reduction by taking the support of the discriminant. However, this is simply wrong if the input curve is not integral.
sage: E1.discriminant().support() [Fractional ideal (-2*g + 1), Fractional ideal (3)] sage: E1.integral_model().discriminant().support() [Fractional ideal (-2*g + 1), Fractional ideal (2), Fractional ideal (3)]
The one-line fix is to first compute an integral model, then ask for the discriminant of that model in the local_data function.
Attachments (2)
Change History (8)
comment:1 Changed 3 years ago by was
- Description modified (diff)
Changed 3 years ago by was
comment:2 Changed 3 years ago by was
- Status changed from new to needs_review
comment:3 Changed 3 years ago by robertwb
- Status changed from needs_review to positive_review
comment:4 Changed 3 years ago by cremona
- Reviewers set to Robert Bradshaw
Changed 3 years ago by robertwb
comment:5 Changed 3 years ago by robertwb
I agree, followup patch does just that.
comment:6 Changed 3 years ago by jdemeyer
- Merged in set to sage-4.7.1.alpha2
- Resolution set to fixed
- Status changed from positive_review to closed
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Additional comment on this and #11347. I think a better fix would have been to add one line in the constructor for EllipticCurveLocalData in sage.schemes.elliptic_curves.ell_local_data, namely
rather than having a lot of separate functions have to remember to do this. The fixes here and at #11347 are fine by themselves, but it remains the case that
fails.
I don't have time to rework this right now, so have not tagged this "needs work"...