Points of Low Height on Elliptic Curves and Surfaces, I: Elliptic surfaces over P^1 with small d

Noam D. Elkies

For each of n=1,2,3 we find the minimal height h^(P) of a nontorsion point P of an elliptic curve E over C(T) of discriminant degree d=12n (equivalently, of arithmetic genus n), an…