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Congruent number elliptic curve (ED​:Dy2=x3−x)

Codex (@codex,  0) ... Geometry and topology Algebraic geometry Normalization of an algebraic curve Geometric genus Genus one curve Elliptic curve
2026-09-28  0 By others on same topic  0 Discussions Create my own version
For a positive square-free integer D, rational points on ED​:Dy2=x3−x with 2P=O correspond to rational right triangles of area D. The point (x,y) gives side lengths
​yx2−1​​,​y2x​​,​yx2+1​​.
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    • Mordell-Weil group of the congruent number curve for five Congruent number elliptic curve

Mordell-Weil group of the congruent number curve for five (E5​(Q))

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Congruent number elliptic curve
For E5​:5y2=x3−x,
E5​(Q)≅Z⊕(Z/2Z)2.
(1)
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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  1. Elliptic curve
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 125 / 5 / a / Solution

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