Some examples of 5 and 7 descent for elliptic curves over $Q$

Fisher, Tom. "Some examples of 5 and 7 descent for elliptic curves over $Q$." Journal of the European Mathematical Society 003.2 (2001): 169-201. <http://eudml.org/doc/277443>.

@article{Fisher2001,
abstract = {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.},
author = {Fisher, Tom},
journal = {Journal of the European Mathematical Society},
keywords = {Mordell-Weil rank; parity conjecture; Tate-Shafarevich group; elliptic curves; descent; Tate-Shafarevich group},
language = {eng},
number = {2},
pages = {169-201},
publisher = {European Mathematical Society Publishing House},
title = {Some examples of 5 and 7 descent for elliptic curves over $Q$},
url = {http://eudml.org/doc/277443},
volume = {003},
year = {2001},
}

TY - JOUR
AU - Fisher, Tom
TI - Some examples of 5 and 7 descent for elliptic curves over $Q$
JO - Journal of the European Mathematical Society
PY - 2001
PB - European Mathematical Society Publishing House
VL - 003
IS - 2
SP - 169
EP - 201
AB - 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.
LA - eng
KW - Mordell-Weil rank; parity conjecture; Tate-Shafarevich group; elliptic curves; descent; Tate-Shafarevich group
UR - http://eudml.org/doc/277443
ER -