#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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Comment(by cremona):
I vote with Alex for 1. This is in fact similar to the following:
{{{
Loading Sage library. Current Mercurial branch is: test2
sage: E = EllipticCurve(ZZ, [1,2,3,4,5])
sage: E.base_ring()
Integer Ring
sage: E.conductor()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
/home/masgaj/.sage/temp/host_56_150/24208/_home_masgaj__sage_init_sage_0.py
in <module>()
AttributeError: 'EllipticCurve_generic' object has no attribute
'conductor'
}}}
as compared to
{{{
sage: E = EllipticCurve([1,2,3,4,5])
sage: E.base_ring()
Rational Field
sage: E.conductor()
10351
}}}
i.e. we already choose to use the field of fractions as base ring when the
entries are integers, and if we try to insist otherwise we get an
ell_generic on which we can do rather little.
Of course a purist would say that there is no such thing as an elliptic
curve over ZZ (it would have to have everywhere good reduction), and we do
not allow singular models.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5856#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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