University of Massachusetts Amherst
	Department of Mathematics and Statistics
	Five College Number Theory Seminar

Abstract: The relation between elliptic curves and the arithmetic-geometric mean (AGM) was discovered Lagrange and Gauss as a method of calculating elliptic integrals. This classical approach is limited to cases where the elliptic curve is given by a cubic equation with three real roots. We define an arithmetic- geometric mean for all elliptic curves over the complex numbers and detail the choices implicit in the classical construction. As time allows, we will look at how these results translate into an AGM for Klein's Quartic Curve, a genus three curve with split Jacobian.