English

Elliptic curves associated with Heron triangles with high $2$-Selmer rank

Number Theory 2023-08-02 v1

Abstract

Rank computation of elliptic curves has deep relations with various unsolved questions in number theory, most notably in the congruent number problem for right-angled triangles. Similar relations between elliptic curves and Heron triangles were established later. In this work, we explicitly compute the 2-Selmer rank of the elliptic curves associated with Heron triangles of even area, which eventually sheds light on the Mordell-Weil rank of those curves.

Keywords

Cite

@article{arxiv.2308.00625,
  title  = {Elliptic curves associated with Heron triangles with high $2$-Selmer rank},
  author = {Vinodkumar Ghale and Md Imdadul Islam and Debopam Chakraborty},
  journal= {arXiv preprint arXiv:2308.00625},
  year   = {2023}
}

Comments

15 pages, 2 tables, comments are welcome