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

[Watson Ladd <watsonbladd@gmail.com>]

On Tue, Dec 23, 2025, 2:53 PM American Citizen <website.reader3@gmail.com> 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