TL;DR: For singular elliptic curves, discrete logarithm problem is easier. In this case it was equivalent to discrete log in the additive group of (F_p, +).

Full writeup at https://gitlab.com/n0tsobad/ctf-writeups/tree/master/2019-02-01-nullcon/Singular

Original writeup (https://gitlab.com/n0tsobad/ctf-writeups/tree/master/2019-02-01-nullcon/Singular).