Explicit moduli for curves of genus 2 with real multiplication by ℚ(√5)
1. Motivation. Let J₀(N) denote the Jacobian of the modular curve X₀(N) parametrizing pairs of N-isogenous elliptic curves. The simple factors of J₀(N) have real multiplication, that is to say that the endomorphism ring of a simple factor A contains an order in a totally real number field of degree dim A. We shall sometimes abbreviate "real multiplication" to "RM" and say that A has maximal RM by the totally real field F if A has an action of the full ring of integers of F. We say that a...