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: |
Description (last modified by )
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
- Description modified (diff)
comment:2 Changed 3 years ago by
- 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
- Description modified (diff)
Note: See
TracTickets for help on using
tickets.