#17295: For elliptic curves over relative number fields, is_isogenous() raises
an
error
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.4
Component: elliptic curves | Keywords: norm absolute relative
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The method `EllipticCurve_number_field.is_isogenous()` computes norms of
ideals of the base field using the `norm()` method. To make this work in
the case where the base field is a relative number field, one has to use
the `absolute_norm()` method instead:
{{{
sage: k.<s> = QuadraticField(2)
sage: K.<b> = k.extension(x^2 - 3)
sage: E = EllipticCurve(k, [-3*s*(4 + 5*s), 2*s*(2 + 14*s + 11*s^2)])
sage: Ec = EllipticCurve(k, [3*s*(4 - 5*s), -2*s*(2 - 14*s + 11*s^2)])
sage: EK = E.base_extend(K)
sage: EcK = Ec.base_extend(K)
sage: EK.is_isogenous(EcK)
Traceback (most recent call last):
...
NotImplementedError: For a fractional ideal in a relative number field you
must use relative_norm or absolute_norm as appropriate
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/17295>
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