Journal of the Ramanujan Mathematical Society
Volume 40, Issue 1, March 2025 pp. 43–71.
Generators for elliptic curves attached to Heron
triangles
Authors:
Yasutsugu Fujita and Tadahisa Nara
Author institution:College of Industrial Technology, Nihon
University, 2-11-1 Shin-ei, Narashino, Chiba, 275-8576, Japan.
Summary:
Goins and Maddox introduced
an elliptic curve associated to Heron triangles,
which are triangles having rational areas with rational three
sides.
We determine the reduction types of the curve.
Further we construct an infinite family of the curve of rank at
least two or three with explicit independent points.
The main results show that the two or three points can be
generators for the rank two or three part of the Mordell–Weil
group on certain conditions.
Contents
Full-Text PDF