id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
15434,elliptic curve isogenies: follow-up to #13615,cremona,,"In #13615 there were major enhancements to the ability to compute isogenies of low degree for elliptic curves. A small bug was found after the ticket was closed and the patched merged into 5.13.beta0:
{{{
sage: K.* = NumberField(x^2+1)
sage: E = EllipticCurve(K,[-2*i-1,0])
sage: E.isogenies_prime_degree(17)
...
ValueError: The polynomial does not define a finite subgroup of the elliptic curve.
}}}
while in fact this curve does have 2 17-isogenies:
{{{
sage: from sage.schemes.elliptic_curves.isogeny_small_degree import isogenies_prime_degree_general
sage: isogenies_prime_degree_general(E,17) # rather slow
[Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-82*i-641)*x over Number Field in i with defining polynomial x^2 + 1,
Isogeny of degree 17 from Elliptic Curve defined by y^2 = x^3 + (-2*i-1)*x over Number Field in i with defining polynomial x^2 + 1 to Elliptic Curve defined by y^2 = x^3 + (-562*i+319)*x over Number Field in i with defining polynomial x^2 + 1]
}}}
This was found by Warwick undergraduate Warren Moore.
This problem can be fixed as follows: in line 1770 of isogeny_small_degree.py replace -27*c4 by -27*c4/1296 (or -c4/48) twice. ",defect,closed,major,sage-5.13,elliptic curves,fixed,,,sage-5.13.beta4,John Cremona,Volker Braun,N/A,,,,,
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