At last, a contributiuon to this thread which actually addresses my
original question!
>> In contrast, it seems sympow is not used by many people. The fact there are
>> no bug reports of it not working on the public servers shows how little it
>> is used. (If someone actually tried to run many of the examples, they will
>> find they don't work).
>
> There is 1 "example" -- the modular degree function -- that is 1000
> times more important than the rest. Here's me *using* sympow:
>
> sage: E = EllipticCurve('5077a'); E
> Elliptic Curve defined by y^2 + y = x^3 - 7*x + 6 over Rational Field
> sage: E.modular_degree()
> 1984
>
This is what I thought. I could provide modular degree from eclib but
it would be *vastly* slower. I myself stopped using my own modular
degree function (despite publishing a paper describing the algorithm,
which I was rather proud of at the time) and started to use sympow
(which was then called ec) for the elliptic curve database, since my
own version took much too long. In fact it is fair to say that for
any elliptic curve not in the database (whose modular degrees are
known and in the database), my implementation would not finish in
reasonable time, which makes my "offer" worth little.
It would be a student project to reimplement Mark W's algorithm (Here:
http://www.emis.ams.org/journals/EM/expmath/volumes/11/11.4/pp487_502.pdf)
.
John
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