Re: question on proving a certain elliptic curve has rank 0

Watson Ladd <[email protected]> Tue, 23 Dec 2025 15:22:06 -0800
Newsgroups gmane.comp.mathematics.pari.user
Message-ID <CACsn0cmdPdAcwewOt8vD=_xUSYUqYhMZW4rs4JPX0e-mYUHJiA@mail.gmail.com>
On Tue, Dec 23, 2025, 2:53 PM American Citizen <[email protected]>
wrote:

> Hello:
>
> According to GP-Pari the elliptic curve (1) has rank = 0.
>
> (1)   y^2 = x^3 + 4*x^2 + 8*x + 8
>
> This curve has torsion 2Z with the torsion point [-2,0]
>
> How can I prove that the curve absolutely has rank = 0?
>

Evaluation of the analytic rank suffices by a result of Coats and Wiles.

>
> Randall
>
>
>
>
> Astra mortemque praestare gradatim