On elliptic curves whose conductor is a product of two prime powers

Sadek, Mohammad

doi:10.1090/S0025-5718-2013-02726-3

On elliptic curves whose conductor is a product of two prime powers
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Math. Comp. 83 (2014), 447-460 Request permission

Abstract:

We find all elliptic curves defined over $\mathbb {Q}$ that have a rational point of order $N,\;N\ge 4$, and whose conductor is of the form $p^aq^b$, where $p,q$ are two distinct primes and $a,b$ are two positive integers. In particular, we prove that Szpiro’s conjecture holds for these elliptic curves.

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