Some improvements to 4-descent on an elliptic curve

Authors:
Tom Fisher
Affiliations:
University of Cambridge, DPMMS, Centre for Mathematical Sciences, Cambridge, UK
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

Citing 5
Cited 0

Theory of algebraic invariants

Theory of algebraic invariants
The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Classical invariants and 2-descent on elliptic curves

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the second Magma conference
Trivializing a central simple algebra of degree 4 over the rational numbers

Journal of Symbolic Computation
Testing equivalence of ternary cubics

ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

The theory of 4-descent on elliptic curves has been developedin the PhD theses of Siksek [18], Womack [21] and Stamminger [20].Prompted by our use of 4-descent in the search for generators of largeheight on elliptic curves of rank at least 2, we explain how to cut downthe number of class group and unit group calculations required, by usingthe group law on the 4-Selmer group.