Premium
Descent Calculations for the Elliptic Curves of Conductor 11
Author(s) -
Fisher Tom
Publication year - 2003
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611502013977
Subject(s) - mathematics , elliptic curve , conductor , pairing , rank (graph theory) , division (mathematics) , supersingular elliptic curve , schoof's algorithm , galois group , descent (aeronautics) , zero (linguistics) , galois module , pure mathematics , combinatorics , geometry , quarter period , arithmetic , physics , linguistics , philosophy , superconductivity , quantum mechanics , meteorology
Let A be any one of the three elliptic curves over Q with conductor 11. We show that A has Mordell–Weil rank zero over its field of 5‐division points. In each case we also compute the 5‐primary part of the Tate–Shafarevich group. Our calculations make use of the Galois equivariance of the Cassels–Tate pairing. 2000 Mathematics Subject Classification 11G05, 11Y40, 11R23.