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  Rational points on an elliptic curve


 This picture illustrates a few rational points on the elliptic curve given by the equation y3 - y = x2 + x and linked by the group law on this curve. The fact that the set of rational points on a non-singular cubic curve admits the structure of an abelian group is fundamental for their arithmetic geometry.


 

© P. Berthelot
Last update : 9.5.04
 

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