#8451: improve galois representation for elliptic curves
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Reporter: wuthrich | Owner: cremona
Type: defect | Status: needs_review
Priority: major | Milestone: sage-4.4
Component: elliptic curves | Keywords: elliptic curves, galois
representation, is_surjective
Author: Chris Wuthrich | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by was):
{{{
[the point of this is to help get this reviewed promptly]
Hi Drew,
If you look in /scratch/drew you'll find a Sage install I created for you:
d...@sage:/scratch/drew/sage-4.4.alpha0-sage.math.washington.edu-x86_64-Linux$
pwd
/scratch/drew/sage-4.4.alpha0-sage.math.washington.edu-x86_64-Linux
It has both #8617, your code, and
http://trac.sagemath.org/sage_trac/ticket/8451 which is the patch you're
refereeing.
The file test.out in that directory will soon contain the output of
running the full sage testsuite with those patches applied:
d...@sage:/scratch/drew/sage-4.4.alpha0-sage.math.washington.edu-x86_64-Linux$
./sage -tp 20 devel/sage/sage/ > test.out&
[1] 12438
Here's using some code:
sage: rho = EllipticCurve('225a').galois_representation()
sage: rho.reducible_primes()
[3]
sage: rho.is_crystalline(3)
False
sage: rho.is_crystalline(5)
False
and your code:
sage: E = EllipticCurve('225a')
sage: E.short_weierstrass_model()
Elliptic Curve defined by y^2 = x^3 + 80 over Rational Field
sage: galrep = sage.libs.galrep.all.GalRep()
sage: galrep.non_surjective_primes(0,80)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]
Another example:
sage: E = EllipticCurve('11a')
sage: E = E.short_weierstrass_model(); E
Elliptic Curve defined by y^2 = x^3 - 13392*x - 1080432 over Rational
Field
sage: galrep.non_surjective_primes(ZZ(E.a4()), ZZ(E.a6()))
[5]
sage: rho = E.galois_representation()
sage: rho.non_surjective()
[5]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8451#comment:9>
Sage <http://www.sagemath.org>
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