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: | |
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Priority: | major | Milestone: | sage-8.5 |

Component: | elliptic curves | Keywords: | |

Cc: | Merged in: | ||

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

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) []

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