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 thath(−D)≥12(c(E)−ε)(logD)r2 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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