Hi Benyamin
To expand on what Jonathan wrote: I coded up his analytic rank bounding
method in Sage as part of my PhD dissertation, and it can be accessed as
Jonathan indicates. There is extensive documentation attached to the code,
so that should help you on your way; however if you have more specific
questions about the implementation I'm happy to correspond with you
directly. FYI the code was used to bound ranks over a large database of
elliptic curves ordered by height (see https://arxiv.org/pdf/1602.01894.pdf);
it's parallelization-ready and fairly well vetted at this point.
Regards
Simon Spicer
On Friday, March 31, 2017 at 6:58:14 AM UTC-7, Jonathan Bober wrote:
>
> This method was implemented by Simon Spicer in Sage and is available as
> the function analytic_rank_upper_bound() attached to an elliptic curve. e.g.
>
> sage: E = EllipticCurve('5077')
> sage: E.analytic_rank_upper_bound()
> 3
>
> so there is no need to try to use psage. Simon's implementation is also
> more general than mine and probably better, though I haven't actually used
> it myself much.
>
> There also exists some simple C++ code that I wrote, e.g. at
> https://github.com/jwbober/psage/blob/master/psage/ellcurve/xxx/ which
> doesn't need anything from sage, and just relies on smalljac, but it is
> less straightforward to use and requires manually specifying values of a_p
> at bad primes. (Without the rankbound.pyx file, you should be able to build
> a standalone binary from that directory, but I haven't done this in a while
> so I don't guarantee anything.)
>
> As for PARI/GP, well, sure, that would be nice, but that's not anything
> I'm going to work on anytime soon. It shouldn't be too hard to write
> something simple.
>
>
> On Thu, Mar 30, 2017 at 4:28 PM, <[email protected] <javascript:>>
> wrote:
>
>> there is an article written by jonathan bober for conditionally upper
>> bound for rank of elliptic curves. based on bsd conjecture and as i know it
>> is implemented in psage , but i dont know how to use it. i registered in
>> psage but can any body say me how to use it ? it also would be very nice to
>> use it in pari / gp
>> thanks
>>
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