Changes between Version 5 and Version 8 of Ticket #26487


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Timestamp:
10/14/18 20:13:31 (2 years ago)
Author:
jdemeyer
Comment:

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  • Ticket #26487

    • Property Commit changed from 58726f355fca49e568673900cda5ce7d7062d47c to 123f2b102cf43184e1c2bcbd5c956152082ea6f1
  • Ticket #26487 – Description

    v5 v8  
    1 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.
    2 
    3 Ordinary:
    4 {{{
    5 sage: E = EllipticCurve(GF(5), [1,1])
    6 sage: E.trace_of_frobenius()
    7 -3
    8 sage: L = E.isogenies_prime_degree(5); L
    9 [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]
    10 }}}
    11 
    12 Supersingular:
    13 {{{
    14 sage: E = EllipticCurve(GF(5), [0,1])
    15 sage: E.trace_of_frobenius()
    16 0
    17 sage: E.isogenies_prime_degree(5)
    18 []
    19 }}}
     1`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. We clarify this in the documentation. We also add some examples and reorganize the existing examples.
    202
    213Additionally, we simplify the logic of the `isogenies_prime_degree()` wrapper a bit.