Alladi Ramakrishnan Hall

The diophantine equation y^2=x^8+x^4+x^2

L. Merel

University of Paris VII

The adjective diophantine here is not employed abusively, as this equation figures
(in ordinary language) in book 6 of Diophantus’ Arithmetica (3rd century BC). We
will explain why it is not easy to determine all rational solutions to this
equation. (All such rational points have been listed by J. Wetherell, though.)

Prerequisite : Some familiarity with elliptic curves (group structure, j-invariant).
Some knowledge of jacobian varieties and of the genus of a curve will be used in the
second half of the talk, but is not required to follow the lecture.