Orders of the torsion of points of curves of genus 1

V. A. Dem'yanenko

Zapiski Nauchnykh Seminarov POMI, Studies in number theory. Part 5, Tome 82 (1979), pp. 5-28

Résumé

Let $K$ be an algebraic number field of degree $n$; $h(K)$ let be the number of divisor classes of the field $K$; $Y:v^2=u^4+au^2+b$ is the Jacobian curve over $K$; $b(a^2-4b)=c^2\prod^N_{i=1}q_i$ where $C$ is an integral divisor, $q_1,\dots,q_N$ are distinct prime divisors. One proves that there exists an effectively computable constant $c=c(n,h(K),N)$, such that the order $m$ of the torsion of any primitive $K$-point on $Y$ is bounded by it: $m\leqslant c$.