On the high rank $π/3$ and $2π/3$-congruent number elliptic curves

Details On the high rank $π/3$ and $2π/3$-congruent number elliptic curves On the high rank $π/3$ and $2π/3$-congruent number elliptic curves

2011-02-21

arxiv.org/abs/1102.4291v1

Mathematics

Number Theory

9 pages, submitted to Journal of Number Theory

Scientific paper

In this article, we try to find high rank elliptic curves in the family $E_{n,\theta}$ defined over $\mathbb Q$ by the equation $y^2=x^3+2snx-(r^2-s^2)n^2x$, where $0 < \theta < \pi$, $\cos(\theta) = s/r$ is rational with $0\leq |s|

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