Elliptic curves and lower bounds for class numbers

2020/01/21 by Griffin, Michael, Ono, Ken
#11G05 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2001.07332

Abstract

Ideal class pairings map the rational points of rank r≥ 1 elliptic curves E/\Q to the ideal class groups \CL(-D) of certain imaginary quadratic fields. These pairings imply that h(-D) ≥ (1)/(2)(c(E)-ε)(log D)^(r)/(2) for sufficiently large discriminants -D in certain families, where c(E) is a natural constant. These bounds are effective, and they offer improvements to known lower bounds for many discriminants.

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