Opened 12 years ago
Closed 12 years ago
#11346 closed defect (fixed)
major bug in the conductor function for elliptic curves over number fields
Reported by: | William Stein | Owned by: | John 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 )
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 12 years ago by
Description: | modified (diff) |
---|
Changed 12 years ago by
Attachment: | trac_11346.patch added |
---|
comment:2 Changed 12 years ago by
Status: | new → needs_review |
---|
comment:3 Changed 12 years ago by
Status: | needs_review → positive_review |
---|
comment:4 Changed 12 years ago by
Authors: | → William Stein |
---|---|
Reviewers: | → Robert Bradshaw |
Changed 12 years ago by
Attachment: | 11346-followup.patch added |
---|
comment:6 Changed 12 years ago by
Merged in: | → sage-4.7.1.alpha2 |
---|---|
Resolution: | → fixed |
Status: | positive_review → closed |
Note: See
TracTickets for help on using
tickets.
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, namelyrather 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"...