MERSENNE PRIME'S FUNCTION IN ELLIPTIC CURVES $y^2=x^3 \pm 3 p x$ AND $y^2=x^3 \pm 6 p x$
Keywords:
Mersenne prime, elliptic curveDOI:
https://doi.org/10.17654/0972555522038Abstract
Under certain conditions, we compute the ranks of elliptic curves $y^2=x^3 \pm 3 p x$ and $y^2=x^3 \pm 6 p x$, denoted by $E_{ \pm 3 p}$ and $E_{ \pm 6 p}$, respectively, where $p$ is a Mersenne prime $p=2^q-1$.
Received: August 7, 2022
Accepted: September 14, 2022
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