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math.NT2001
Appendix to a paper of Maisner and Nart
Everett W. Howe
We prove that there is no genus-2 curve over F_q whose Jacobian has characteristic polynomial of Frobenius equal to x^4 + (1 - 2q) x^2 + q^2. Maisner and Nart had observed (by dire…
math.NT2001
On the group orders of elliptic curves over finite fields
Everett W. Howe
Given a prime power q, for every pair of positive integers m and n with m dividing the GCD of n and q-1, we construct a modular curve over F_q that parametrizes elliptic curves ove…