Bring's Curve: its Period Matrix and the Vector of Riemann Constants - Braden, H.W.; Northover, T.P. (Symmetry, Integrability and Geometry: Methods and Applications, 2012)
Bring's curve is the genus 4 Riemann surface with automorphism group of maximal size, S₅. Riera and Rodríguez have provided the most detailed study of the curve thus far via a hyperbolic model. We will recover and extend their results via an algebraic model based on a sextic curve given by both Hulek and Craig and implicit in work of Ramanujan. In particular we recover their period matrix; further, the vector of Riemann constants will be identified.