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On the frequency of finitely anomalous elliptic curves

Penny C Ridgdill, University of Massachusetts Amherst


Given an elliptic curve E over [special characters omitted], we can then consider E over the finite field Fp. If Np is the number of points on the curve over Fp, then we define ap(E) = p + 1 − Np. We say primes p for which ap( E) = 1 are anomalous. In this paper, we search for curves E so that this happens for only a finite number of primes. We call such curves finitely anomalous. This thesis deals with the frequency of their occurrence and finds several examples.

Subject Area


Recommended Citation

Ridgdill, Penny C, "On the frequency of finitely anomalous elliptic curves" (2010). Doctoral Dissertations Available from Proquest. AAI3409647.