Opened 3 years ago

Last modified 2 years ago

#26487 closed defect

Document that isogenies_prime_degree() only finds separable isogenies — at Version 3

Reported by: jdemeyer Owned by:
Priority: major Milestone: sage-8.5
Component: elliptic curves Keywords:
Cc: Merged in:
Authors: Jeroen Demeyer Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by jdemeyer)

It seems that isogenies_prime_degree only finds separable isogenies, so it never finds the Frobenius. This is not documented very well. 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)
[]

Additionally, we simply the logic of the isogenies_prime_degree() wrapper a bit.

Change History (3)

comment:1 Changed 3 years ago by jdemeyer

  • Description modified (diff)

comment:2 Changed 3 years ago by jdemeyer

  • Authors set to Jeroen Demeyer
  • Description modified (diff)
  • Summary changed from isogenies_prime_degree() does not work well for degree = characteristic to Document that isogenies_prime_degree() only finds separable isogenies

comment:3 Changed 3 years ago by jdemeyer

  • Description modified (diff)
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