Geodesic
Some examples of 5 and 7 descent for elliptic curves over Q
Journal of the European Mathematical Society, Tome 3 (2001) no. 2, pp. 169-201

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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.
DOI : 10.1007/s100970100030
Classification : 11-XX, 14-XX, 20-XX, 00-XX
Keywords: 
@article{JEMS_2001_3_2_a2,
     author = {Tom Fisher},
     title = {Some examples of 5 and 7 descent for elliptic curves over {Q}},
     journal = {Journal of the European Mathematical Society},
     pages = {169--201},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2001},
     doi = {10.1007/s100970100030},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970100030/}
}
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Tom Fisher. Some examples of 5 and 7 descent for elliptic curves over Q. Journal of the European Mathematical Society, Tome 3 (2001) no. 2, pp. 169-201. doi: 10.1007/s100970100030

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