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

 

Elliptic curves with nonsplit mod $11$ representations


Authors: Imin Chen and Chris Cummins
Journal: Math. Comp. 73 (2004), 869-880
MSC (2000): Primary 11G05; Secondary 14G05
Published electronically: June 17, 2003
MathSciNet review: 2031412
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Abstract: We calculate explicitly the $j$-invariants of the elliptic curves corresponding to rational points on the modular curve $X_{ns}^+(11)$ by giving an expression defined over $\mathbb{Q} $ of the $j$-function in terms of the function field generators $X$ and $Y$of the elliptic curve $X_{ns}^+(11)$. As a result we exhibit infinitely many elliptic curves over $\mathbb{Q} $ with nonsplit mod $11$representations.


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Additional Information

Imin Chen
Affiliation: Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6
Email: ichen@math.sfu.ca

Chris Cummins
Affiliation: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, Canada, H3G 1M8
Email: cummins@mathstat.concordia.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01562-X
PII: S 0025-5718(03)01562-X
Received by editor(s): May 2, 2002
Received by editor(s) in revised form: September 11, 2002
Published electronically: June 17, 2003
Additional Notes: Research supported by NSERC
Article copyright: © Copyright 2003 American Mathematical Society