Submitted:
30 January 2021
Posted:
01 February 2021
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Abstract
We show that if the quadratic twist family of a given elliptic curve over F_q[t] with char(F_q) > 5 has an element whose Neron model has a multiplicative reduction away from infinity, then the average p-Selmer rank is p+1 in large q-limit for almost all primes p.
Keywords:
Selmer group
; quadratic twist
; elliptic curve
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