- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
3
2001
2
Some examples of 5 and 7 descent for elliptic curves over Q
Tom
Fisher
University of Cambridge, CAMBRIDGE, UNITED KINGDOM
We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over Q may become arbitrarily large.
Number theory
Algebraic geometry
Group theory and generalizations
General
169
201
10.1007/s100970100030
http://www.ems-ph.org/doi/10.1007/s100970100030