A K3 surface related to Leonardo Pisano's work on congruent numbers

Abstract

This note recalls an early 13th century result on congruent numbers by Leonardo Pisano (“Fibonacci”), and shows how it relates to a specific much studied K3 surface and to an elliptic fibration on this surface. As an aside, the discussion reveals how, via explicit maps of degree two, the surface is covered by the Fermat quartic surface and also covers one of the two famous ‘most algebraic K3 surfaces’.