On $p$-degree of elliptic curves

Jędrzej Garnek

doi:10.1142/S1793042118500434

On $p$-degree of elliptic curves

Number Theory 2017-09-25 v2 Algebraic Geometry

Authors: Jędrzej Garnek

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Abstract

In this note we investigate the $p$ -degree function of elliptic curves over the field $\mathbb{Q}_p$ of $p$ -adic numbers. The $p$ -degree measures the least complexity of a non-zero $p$ -torsion point on an elliptic curve. We prove some properties of this function and compute it explicitly in some special cases.

Keywords

elliptic curves p-degree p-adic numbers p-torsion point number theory

Cite

@article{arxiv.1701.08822,
  title  = {On $p$-degree of elliptic curves},
  author = {Jędrzej Garnek},
  journal= {arXiv preprint arXiv:1701.08822},
  year   = {2017}
}

Comments

14 pages

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