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

Journal of the European Mathematical Society (2001)

- Volume: 003, Issue: 2, page 169-201
- ISSN: 1435-9855

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topFisher, 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 -

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