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Title: Ordinary elliptic curves of high rank over Fp(x) with constant j-invariant
Authors: Bouw, II ×
Diem, C
Scholten, Jasper #
Issue Date: 2004
Publisher: Springer-Verlag
Series Title: Manuscripta Mathematica vol:114 issue:4 pages:487-501
Abstract: We show that under the assumption of Artin's Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over (F) over bar (p)(x) with arbitrarily high rank and constant j-invariant. For odd primes p, this result follows from a theorem we prove which states that whenever p is a generator of (Z/lZ)*/<-1> (l an odd prime) there exists a hyperelliptic curve over (D) over bar (p) whose Jacobian is isogenous to a power of one ordinary elliptic curve.
URI: 
ISSN: 0025-2611
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
× corresponding author
# (joint) last author

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