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An elliptic curve is an algebraic curve of genus one with some additional properties. Questions with this tag will often have the top-level tags nt.number-theory or ag.algebraic-geometry. Note also the tag arithmetic-geometry as well as some related tags such as rational-points, abelian-varieties, heights. Please do not use this tag for questions related to ellipses; instead use conic-sections.

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On Euler's elliptic curve for $A^4+B^4 = C^4+D^4$?

This is a partial answer. Using the group law of elliptic curves, we have, $b_{10}=\frac{\left(n^{102}+133370 n^{100}+235431945 n^{98}-53960558412 n^{96}+\,\dots\,+607383986505 n^{6}+2125016730 n^{4}- …
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