#19840: Bug in elliptic curve isogeny
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.0
Component: elliptic curves | Keywords: isogenies
Merged in: | Authors: John Cremona
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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There is a bug in the code to compute 5-isogenies of elliptic curves of
j-invariant 1728, when 5 is a square.
{{{
sage: K.<a> = NumberField(x^4 - 5*x^2 + 5)
sage: E = EllipticCurve([a^2 + a + 1, a^3 + a^2 + a + 1, a^2 + a,
17*a^3 + 34*a^2 - 16*a - 37, 54*a^3 + 105*a^2 - 66*a - 135])
sage: E.j_invariant()
1728
sage: K(5).is_square()
True
sage: E.isogenies_prime_degree(5)
ValueError: The polynomial does not define a finite subgroup of the
elliptic curve.
}}}
or more directly
{{{
sage: from sage.schemes.elliptic_curves.isogeny_small_degree import
isogenies_5_1728
sage: isogenies_5_1728(E)
ValueError: The polynomial does not define a finite subgroup of the
elliptic curve.
}}}
I wrote this code about 5 years ago, and will fix it.
--
Ticket URL: <http://trac.sagemath.org/ticket/19840>
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