Bill Allombert on Fri, 20 Jan 2017 10:11:36 +0100

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Re: Pari

On Fri, Jan 20, 2017 at 10:38:21AM +0330, Benyamin Gholami wrote:
> Hi . i work with elliptic  curves and i want to calculate rank of elliptic
> curves  with Pari but i don't know it's code. can anybody help me?.

In PARI you can use
ellanalyticrank(E) to compute the analytic rank

If you have the elldata package installed and your curve has conductor
less than 400000, then you can use
#ellgenerators() to get the group rank from Cremona database.

Otherwise you can use Denis Simon program ellQ:

Or John Cremona mwrank (using extern):

Currently, there is no direct way to compute the group rank in PARI.

> in general i want a perfect catalouge for elliptc curves computing with pari

I suggest these links:

A tutorial about elliptic curve:

The reference card about elliptic curve: