#9409: Bug in elliptic curves method .count_points() over finite fields
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Reporter: adam | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone:
Component: elliptic curves | Keywords: Elliptic Curves .count_points()
Author: Adam Sorkin | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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There is some bug in the method .count_points() which belongs to elliptic
curves defined over finite fields. This might be specific to EC defined
over number fields - I only get this error when I take an EC over a number
field, reduce at a good prime and then count points. In fact, I get the
correct answer the first time, but if I define a second EC over a possibly
different number field and count points at a good reduction, then the
method .count_points() fails. I suspect this has to do with the
cacheing...
If you want to reproduce the behavior, try the following code:
### this just runs through the method outlined above:
def test(curve, bound):
for i in primes(bound):
print "Checking primes over %d: "%i
factors = curve.base_field().ideal(i).factor()
for j in range(len(factors)):
if curve.has_good_reduction(factors[j][0]):
if factors[j][0].divides(curve.discriminant()):
print "Curve has good reduction, but this isn't not a
minimal model",
print "at %s with %d points in the reduced
curve"%(factors[j][0],
curve.local_minimal_model(factors[j][0]).reduction(factors[j][0]).count_points()
)
else:
print "Curve has good reduction and is a minimal
model"
print "at %s with %d points in the reduced
curve"%(factors[j][0], curve.reduction(factors[j][0]).count_points() )
else:
print "Curve has bad reduction over %s"%factors[j][0]
return
### sample 1
K.<t> = NumberField(x^2 + 1); E = EllipticCurve(K, [0, 1, 0, -2*t - 2,
2*t]); E
### sample 2
L.<u> = NumberField(x^2 - 2); F = EllipticCurve(L, [0,2,0, 2*u +4, 2*u +
3]); F
test(E, 100)
## now the error will happen
test(F, 100)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9409>
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