Elliptic dilogarithms and parallel lines

TL;DR

This paper proves Boyd's conjectures connecting Mahler's measures and elliptic curve L-values specifically for elliptic curves with conductor 14, advancing understanding of these mathematical relationships.

Contribution

It provides a proof of Boyd's conjectures for elliptic curves of conductor 14, a previously unresolved case, linking Mahler measures to elliptic L-functions.

Findings

Confirmed Boyd's conjectures for conductor 14 elliptic curves

Established explicit relationships between Mahler measures and L-values

Enhanced understanding of elliptic curve invariants

Abstract

We prove Boyd's conjectures relating Mahler's measures and values of L-functions of elliptic curves in the cases when the corresponding elliptic curve has conductor 14.