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

Mohammad Sadek

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

Number Theory 2013-10-30 v2

Authors: Mohammad Sadek

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, a, b are two positive integers. In particular, we prove that Szpiro's conjecture holds for these elliptic curves.

Keywords

elliptic curves rational point order conductor Szpiro's conjecture

Cite

@article{arxiv.1206.3715,
  title  = {On elliptic curves whose conductor is a product of two prime powers},
  author = {Mohammad Sadek},
  journal= {arXiv preprint arXiv:1206.3715},
  year   = {2013}
}

Comments

18 pages

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