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Mathematics of Computation

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


Author: Mohammad Sadek
Journal: Math. Comp. 83 (2014), 447-460
MSC (2010): Primary 14H52
DOI: https://doi.org/10.1090/S0025-5718-2013-02726-3
Published electronically: June 14, 2013
MathSciNet review: 3120599
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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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Additional Information

Mohammad Sadek
Affiliation: Department of Mathematics and Actuarial Science, American University in Cairo, New Cairo, Egypt 11835
Email: mmsadek@aucegypt.edu

DOI: https://doi.org/10.1090/S0025-5718-2013-02726-3
Received by editor(s): February 27, 2012
Published electronically: June 14, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.