constructing elliptic curves

[John Cremona]

Bill Allombert on pari-dev pointed out that Sage's current behaviour
of, when construction an elliptic curve over Q from a j-invariant,
automatically finding the minimal quadratic twist, has the side-effect
of factoring j and j-1728, which adds to the complexity of what would
otherwise be a trivial operation. (See lines 423-455 of
sage/schemes/elliptic_curves/constructor.py.) So perhaps we should
either not do this at all, or have it as an option. It would be easy
to do that in the function that does the work, EllipticCurve_from_j(),
but less natural with normal route via EllipticCurve(j=...) which
would also need a new parameter to be passed to the other function.

Any thoughts?

John

[David Roe]

We could have a "minimal_twist" option to the EllipticCurve constructor, which would be false by default.
David

John

--
You received this message because you are subscribed to the Google Groups "sage-nt" group.
To post to this group, send an email to sag...@googlegroups.com.
To unsubscribe from this group, send email to sage-nt+u...@googlegroups.com.
For more options, visit this group at http://groups.google.com/group/sage-nt?hl=en-GB.

[William Stein]

On Sat, Jun 9, 2012 at 5:02 PM, David Roe <roed...@gmail.com> wrote:
> We could have a "minimal_twist" option to the EllipticCurve constructor,
> which would be false by default.
> David

I think it should be *true* by default, for backwards compatibility,
and because usually this is what you want (nobody has complained).
We should definitely have both a fast and less clean version (like
PARI no doubt will default to), and a nicer but slower version (that
pari will probably never have), and the nice version should I think be
the default.

--
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

[John Cremona]

Thanks -- I have created ticket #13100 for this and will deal with it,
as well as #11773 while I am at it (but with separate patches). Just
don't mention #128.

John