Reference : Effective Kummer Theory for Elliptic Curves
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Physical, chemical, mathematical & earth Sciences : Mathematics
Effective Kummer Theory for Elliptic Curves
Lombardo, Davide mailto [Università di Pisa > Dipartimento di Matematica]
Tronto, Sebastiano mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
[en] Elliptic curves ; Kummer Theory
[en] Let E be an elliptic curve defined over a number field K, let α ∈ E(K) be a point of infinite
order, and let N −1 α be the set of N -division points of α in E(K). We prove strong effective
and uniform results for the degrees of the Kummer extensions [K(E[N ], N −1 α) : K(E[N ])].
When K = Q, and under a minimal (necessary) assumption on α, we show that the inequality
[Q(E[N ], N −1 α) : Q(E[N ])] ≥ cN 2 holds with a constant c independent of both E and α.

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