The database currently contains 66,158 genus 2 curves over $\Q$ of absolute discriminant up to 1,000,000. Here are some further statistics.
Browse genus 2 curves over $\Q$
By conductor: 1-499 500-999 1000-99999 100000-1000000
By absolute discriminant: 1-499 500-999 1000-99999 100000-1000000
Some of our favorite curves: 169.a.169.1 1116.a.214272.1 11664.a.11664.1 1369.a.50653.1 15360.f.983040.2
A random genus 2 curve from the database.