Opened 3 years ago

Last modified 2 years ago

#26487 closed defect

isogenies_prime_degree() does not work well for degree = characteristic — at Version 1

Reported by: jdemeyer Owned by:
Priority: major Milestone: sage-8.5
Component: elliptic curves Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
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Description (last modified by jdemeyer)

Depending on how ambitious one is, this is either a documentation bug or a missing feature. It seems that isogenies_prime_degree only finds separable isogenies, so it never finds the Frobenius. It does find the Verschiebung for ordinary elliptic curves but not for supersingular elliptic curves.

Ordinary:

sage: E = EllipticCurve(GF(5), [1,1])
sage: E.trace_of_frobenius()
-3
sage: L = E.isogenies_prime_degree(5); L
[Isogeny of degree 5 from Elliptic Curve defined by y^2 = x^3 + x + 1 over Finite Field of size 5 to Elliptic Curve defined by y^2 = x^3 + x + 4 over Finite Field of size 5]

Supersingular:

sage: E = EllipticCurve(GF(5), [0,1])
sage: E.trace_of_frobenius()
0
sage: E.isogenies_prime_degree(5)
[]

Change History (1)

comment:1 Changed 3 years ago by jdemeyer

  • Description modified (diff)
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