✦ LIBER ✦

On the Cyclicity of the Group of Fp-Rational Points of Non-CM Elliptic Curves

✍ Scribed by Alina Carmen Cojocaru

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 143 KB
Volume: 96
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2002.2789

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✦ Synopsis

Let E be an elliptic curve defined over Q and without complex multiplication. For a prime p of good reduction, let % E E be the reduction of E modulo p: Assuming that certain Dedekind zeta functions have no zeros in ReðsÞ > 3=4; we determine how often % E EðF p Þ is a cyclic group. This result was previously obtained by J.-P. Serre using the full Generalized Riemann Hypothesis for the same Dedekind zeta functions considered by us.

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