Minimal number of points with bad reduction for elliptic curves over P^1

TL;DR

This paper investigates the minimal number of points with bad reduction for non-constant elliptic curves over the projective line, using elementary methods to address a fundamental question in the arithmetic of elliptic curves.

Contribution

It provides an elementary approach to determine the minimal bad reduction points for elliptic curves over P^1 with non-constant j-invariant.

Findings

Identifies the minimal number of bad reduction points for certain elliptic curves.

Provides bounds and conditions for bad reduction points.

Uses elementary methods to analyze elliptic curve reductions.

Abstract

In this work we use elementary methods to discuss the question of the minimal number of points with bad reduction over the projective line for elliptic curves E/k(T) which are non-constant resp. have non-constant j-invariant.