Ordinary elliptic curves of high rank over Fp(x) with constant j-invariant
نویسندگان
چکیده
We show that under the assumption of Artin’s Primitive Root Conjecture, for all primes p there exist ordinary elliptic curves over Fp(x) with arbitrary high rank and constant j-invariant. For odd primes p, this result follows from a theorem which states that whenever p is a generator of (Z/lZ)∗/〈−1〉 (l an odd prime) there exists a hyperelliptic curve over Fp whose Jacobian is isogenous to a power of one ordinary elliptic curve.
منابع مشابه
Ordinary elliptic curves of high rank over Fp(x) with constant j-invariant II
We show that for all odd primes p, there exist ordinary elliptic curves over Fp(x) with arbitrarily high rank and constant j-invariant. This shows in particular that there are elliptic curves with arbitrarily high rank over these fields for which the corresponding elliptic surface is not supersingular. The result follows from a theorem which states that for all odd prime numbers p and l, there ...
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تاریخ انتشار 2003