On Tate-Shafarevich groups of some elliptic curves

Details On Tate-Shafarevich groups of some elliptic curves On Tate-Shafarevich groups of some elliptic curves

1999-03-18

arxiv.org/abs/math/9903208v1

Mathematics

Number Theory

Scientific paper

This is an updated version of ANT-0166.
Generalizing results of Stroeker and Top we show that the 2-ranks of the
Tate-Shafarevich groups of the elliptic curves $y^2 = (x+k)(x^2+k^2)$ can
become arbitrarily large. We also present a conjecture on the rank of the
Selmer groups attached to rational 2-isogenies of elliptic curves.

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