CLASS NUMBERS VIA 3-ISOGENIES AND ELLIPTIC SURFACES
CAM McLEMAN
Department of Mathematics, University of Michigan-Flint, Flint, MI 42439, USA
DUSTIN MOODY
National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, MD, 20899, USA
Received: 24 April 2012
Accepted: 25 June 2012
Published: 6 November 2012
We show that a character sum attached to a family of 3-isogenies defined on the fibers of a certain elliptic surface over 𝔽p relates to the class number of the quadratic imaginary number field 
Keywords: Elliptic curve; elliptic surface; class number; character sum
AMSC: 11T24, 14J27, 11R29