Work

Explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields

Year: 2026

Type: article

Abstract: Following the work of Mestre, we use Weil's explicit formulas to compute explicit lower bounds on the conductors of elliptic curves and abelian varieties over number fields, assuming that their associated L -functions are analytic L -functions. Moreover, we obtain lower bounds for the conductor of elliptic curves and abelian varieties over Q with specified bad reduction, under the same hypothesis. As an application, we prove, for certain number fields, the non-existence of abelian varieties with analytic L -function and with everywhere good reduction.

Source: Journal of Number Theory

DOI: 10.1016/j.jnt.2026.06.014

Author: Pierre Tchamitchian

Institutions: Aix-Marseille Université, Institut de Mathématiques de Marseille

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Aix-Marseille Université