4 papers · 1 filter
The probability of isomorphic group structures of isogenous elliptic curves over finite fields
John Cullinan, Nathan Kaplan
Let l be a prime number and let E and E' be l-isogenous elliptic curves defined over Q. In this paper we determine the proportion of primes p for which E(F_p) is isomorphic to E'(F…
Tamagawa Numbers of Elliptic Curves with an -isogeny
Alexander Barrios, John Cullinan
Let be an odd prime, and suppose is an elliptic curve defined over the rational numbers . If has an -torsion point, then there has been significant…
On the discriminants of truncated logarithmic polynomials
John Cullinan, Rylan Gajek-Leonard
We provide evidence for a conjecture of Yamamura that the truncated logarithmic polynomials \[ F_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n} \] have Galois group fo…
The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, II
John Cullinan, Shanna Dobson, Linda Frey +5
Let and be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq…