Trisections and cubes in elliptic curves
Loading...
Date
2023
Authors
Pujolàs Boix, Jordi
Thériault, Nicolas
Other authors
Impact
Export
Share
Journal Title
Journal ISSN
Volume Title
Abstract
We show how to compute the pre-images of multiplication by 3 in the group of points
of an elliptic curve E over a field k of characteristic different from 2 and 3 such that
E[3](k) = E[3]. We show Q = (xQ, yQ) ∈ [3]E(k) if and only if yQ − d − m(xQ − c)
is a cube in k for every 3-torsion point (c, d) ∈ E[3], where m is the slope of the
tangent to E at (c, d). We reduce our problem to the computation of at most 2
independent cubic roots plus a few polynomial operations.
Related resource
Citation
Journal or Serie
Journal of Pure and Applied Algebra, 2023, vol. 227, núm. 4, 107259