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