Computing rational points
on rank 1 elliptic curves
via -series and canonical heights
Author:
Joseph H. Silverman
Journal:
Math. Comp. 68 (1999), 835-858
MSC (1991):
Primary 11G05, 11Y50
DOI:
https://doi.org/10.1090/S0025-5718-99-01068-6
MathSciNet review:
1627825
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an elliptic curve of rank 1. We describe an algorithm which uses the value of
and the theory of canonical heghts to efficiently search for points in
and
. For rank 1 elliptic curves
of moderately large conductor (say on the order of
to
) and with a generator having moderately large canonical height (say between 13 and 50), our algorithm is the first practical general purpose method for determining if the set
contains non-torsion points.
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Additional Information
Joseph H. Silverman
Affiliation:
Mathematics Department, Box 1917, Brown University, Providence, RI 02912 USA
Email:
jhs@gauss.math.brown.edu
DOI:
https://doi.org/10.1090/S0025-5718-99-01068-6
Keywords:
Elliptic curve,
canonical height
Received by editor(s):
May 8, 1996
Received by editor(s) in revised form:
March 3, 1997
Additional Notes:
Research partially supported by NSF DMS-9424642.
Article copyright:
© Copyright 1999
American Mathematical Society