Abstract
Let E and E′ be 2-isogenous elliptic curves over Q. Following [6], we call a prime of good reduction p anomalous if E(Fp)≃E′(Fp) but E(Fp2)≄E′(Fp2). Our main result is an explicit formula for the proportion of anomalous primes for any such pair of elliptic curves. We consider both the CM case and the non-CM case.
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