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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Equations for the modular curve $ X_1(N)$ and models of elliptic curves with torsion points

Author: Houria Baaziz
Journal: Math. Comp. 79 (2010), 2371-2386
MSC (2010): Primary 11F03; Secondary 11G05, 11G18, 11G30
Published electronically: April 16, 2010
MathSciNet review: 2684370
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Abstract: We describe an algorithm for constructing plane models of the modular curve $ X_1(N)$ and discuss the resulting equations when $ N\leq 51$.

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Additional Information

Houria Baaziz
Affiliation: USTHB Faculté de Mathématiques, BP 32 El Alia Bab Ezzouar Alger, 16111 Algeria

PII: S 0025-5718(10)02332-X
Keywords: Modular curves, elliptic curves, torsion points
Received by editor(s): August 29, 2008
Received by editor(s) in revised form: July 17, 2009
Published electronically: April 16, 2010
Additional Notes: This work was done at the Laboratoire de Mathématiques Nicolas Oresme of the University of Caen. I am deeply indebted to Professor John Boxall for advice and encouragement during my stay at the University of Caen. I am grateful to all members of the Laboratory for their reception and for the provision of facilities. Finally, I would like to thank the referee for his helpful comments on an earlier version of the paper.
Article copyright: © Copyright 2010 American Mathematical Society