#16957: sorting elliptic curves with the same conductor over number fields
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Reporter: ArgaezG | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #16743 | Stopgaps:
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Comment (by cremona):
We decided not to do this. If you factor the L-functions into Euler
products by the primes of the field K then you have to sort the primes of
each norm, a problem in itself. If you just factor over Q then conjugate
curves have the same L-function.
What Sage currently does is this: the curves in an isogeny class almost
always have distinct j-invariants, so we first sort by j-invariant (using
the method for sorting number field elements already in Sage). Usually
that is enough, which is good since then the order is independent of the
Weierstrass models. The only case when it is not enough is when E has
potential CM, as then it is isogenous to its quadratic twist by the
relevant CM field but not isomorphic (that is what "potential" means). In
that case we use the vector of a-invariants for sorting; in which case the
order will in general depend on which Weierstrass models are used, which
is unfortunate, but no-one has yet come up with a better tie-break.
--
Ticket URL: <http://trac.sagemath.org/ticket/16957#comment:1>
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