Opened 3 years ago

Last modified 2 years ago

## #26487 closed defect

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

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: | ||

Dependencies: | Stopgaps: |

### Description

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 (where it's found multiple times somehow) 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, 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, 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, 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, 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] sage: L[0] == L[1] True

Supersingular:

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

**Note:**See TracTickets for help on using tickets.