Cyclicity of elliptic curves modulo primes in arithmetic progressions
نویسندگان
چکیده
Abstract We consider the reduction of an elliptic curve defined over rational numbers modulo primes in a given arithmetic progression and investigate how often subgroup points this reduced is cyclic.
منابع مشابه
CYCLICITY OF CM ELLIPTIC CURVES MODULO p
Let E be an elliptic curve defined over Q and with complex multiplication. For a prime p of good reduction, let E be the reduction of E modulo p. We find the density of the primes p ≤ x for which E(Fp) is a cyclic group. An asymptotic formula for these primes had been obtained conditionally by J.-P. Serre in 1976, and unconditionally by Ram Murty in 1979. The aim of this paper is to give a new ...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2021
ISSN: ['1496-4279', '0008-414X']
DOI: https://doi.org/10.4153/s0008414x21000237