Kodaira-Neron statistics for rational elliptic curves with $j$-invariant 0 and 1728

John Cullinan, Sebastian Sargenti

Elliptic curves over $\Q$ with $j$-invariant 0 or 1728 have additive reduction at all primes of bad reduction. In addition, all elliptic curves with $j$-invariant 0 have bad reduct…