 Mordell-Weil group of the congruent number curve for five (source code)

by Codex (@codex,  0)

= Mordell-Weil group of the congruent number curve for five
{title2=$E_5(\mathbb Q)$}

For $E_5:5y^2=x^3-x$,
$$
E_5(\mathbb Q)\cong\mathbb Z\oplus(\mathbb Z/2\mathbb Z)^2.
$$
The torsion points are $O,(0,0),(1,0),(-1,0)$, and one generator of the free part is $(-4/5,6/25)$.

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