#5856: elliptic curves over Z/pZ are treated totally differently than elliptic
curves over GF(p)
---------------------------+------------------------------------------------
Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.2
Component: number theory | Keywords:
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Description changed by was:
Old description:
> We have
> {{{
> sage: type(EllipticCurve(Zmod(11), [1,2]))
> <class 'sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic'>
> sage: type(EllipticCurve(GF(11), [1,2]))
> <class
> 'sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field'>
> }}}
>
> This means that if you make a curve over Z/pZ then basically nothing
> works, but if you make the same curve over GF(p), there is tons of
> functionality.
New description:
We have
{{{
sage: type(EllipticCurve(Zmod(11), [1,2]))
<class 'sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic'>
sage: type(EllipticCurve(GF(11), [1,2]))
<class
'sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field'>
}}}
See also #5857.
This means that if you make a curve over Z/pZ then basically nothing
works, but if you make the same curve over GF(p), there is tons of
functionality.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5856#comment:1>
Sage <http://sagemath.org/>
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