The database currently contains 66,158 genus 2 curves in 65,534 isogeny classes, with absolute discriminant at most 1,000,000.

## Distribution of rational points

 rational points count proportion rational points count proportion rational points count proportion 0 1 2 3 4 5 6 7 8 9 5140 6454 11575 8719 9434 5089 6561 2967 3911 1328 7.77% 9.76% 17.50% 13.18% 14.26% 7.69% 9.92% 4.48% 5.91% 2.01% 10 11 12 13 14 15 16 17 18 19 1926 578 1130 234 574 97 276 28 103 2 2.91% 0.87% 1.71% 0.35% 0.87% 0.15% 0.42% 0.04% 0.16% 0.00% 20 21 22 24 26 $$\mathrm{avg}\ 4.25$$ 20 1 3 6 2 66158 0.03% 0.00% 0.00% 0.01% 0.00% 100.00%

## Distribution of rational Weierstrass points

 Weierstrass points count proportion 0 1 2 3 4 $$\mathrm{avg}\ 0.66$$ 32616 24611 8005 886 40 66158 49.30% 37.20% 12.10% 1.34% 0.06% 100.00%

## Distribution of $\mathrm{Aut}(X)$

 automorphism group count proportion $D_6$ $C_2$ $C_4$ $C_2^2$ $C_6$ $D_4$ 4 63480 15 2597 58 4 0.01% 95.95% 0.02% 3.93% 0.09% 0.01%

## Distribution of $\mathrm{Aut}(X_{\overline{\mathbb{Q}}})$

 automorphism group count proportion $C_{10}$ $D_6$ $C_2$ $C_3:D_4$ $C_2^2$ $\GL(2,3)$ $D_4$ 5 88 63310 4 2698 3 50 0.01% 0.13% 95.70% 0.01% 4.08% 0.00% 0.08%

## Distribution of analytic ranks

 analytic rank count proportion 0 1 2 3 4 $$\mathrm{avg}\ 1.21$$ 12131 30579 20561 2877 10 66158 18.34% 46.22% 31.08% 4.35% 0.02% 100.00%

## Distribution of 2-Selmer ranks

 2-Selmer rank count proportion 0 1 2 3 4 5 6 $$\mathrm{avg}\ 1.62$$ 3878 25496 29403 6879 448 49 5 66158 5.86% 38.54% 44.44% 10.40% 0.68% 0.07% 0.01% 100.00%

## Distribution of squareness of Ш

has square Ш count False True 2284 63874 3.45% 96.55%

## Distribution of analytic order of Ш

 analytic order of Ш count proportion analytic order of Ш count proportion 1 2 4 8 9 16 18 32 36 49 61950 2233 1790 45 46 78 2 3 6 1 93.64% 3.38% 2.71% 0.07% 0.07% 0.12% 0.00% 0.00% 0.01% 0.00% 50 64 256 $$\mathrm{avg}\ 1.16$$ 1 2 1 66158 0.00% 0.00% 0.00% 100.00%

## Distribution of local solvability

locally solvable count False True 3371 62787 5.10% 94.90%

## Distribution of $\mathrm{GL}_2$-type

is of GL2-type count False True 63312 2846 95.70% 4.30%

## Distribution of Sato-Tate group identity components

 identity component count proportion $$\mathrm{U}(1)\times\mathrm{U}(1)$$ $$\mathrm{U}(1)\times\mathrm{SU}(2)$$ $$\mathrm{U}(1)$$ $$\mathrm{SU}(2)$$ $$\mathrm{USp}(4)$$ $$\mathrm{SU}(2)\times\mathrm{SU}(2)$$ 6 303 8 150 63107 2584 0.01% 0.46% 0.01% 0.23% 95.39% 3.91%

## Distribution of Sato-Tate groups

 Sato-Tate group count proportion Sato-Tate group count proportion $D_{2,1}$ $D_{3,2}$ $D_{6,2}$ $E_1$ $E_2$ $E_3$ $E_4$ $E_6$ $F_{ac}$ $J(C_2)$ 3 1 1 8 3 7 10 51 6 2 0.00% 0.00% 0.00% 0.01% 0.00% 0.01% 0.02% 0.08% 0.01% 0.00% $J(C_4)$ $J(E_1)$ $J(E_2)$ $J(E_3)$ $J(E_4)$ $J(E_6)$ $N(\mathrm{SU}(2)\times\mathrm{SU}(2))$ $N(\mathrm{U}(1)\times\mathrm{SU}(2))$ $\mathrm{SU}(2)\times\mathrm{SU}(2)$ $\mathrm{USp}(4)$ 1 24 9 4 17 17 144 303 2440 63107 0.00% 0.04% 0.01% 0.01% 0.03% 0.03% 0.22% 0.46% 3.69% 95.39%

## Distribution of torsion subgroup orders

 torsion order count proportion torsion order count proportion torsion order count proportion 1 2 3 4 5 6 7 8 9 10 44190 14681 2295 2754 725 595 97 393 38 131 66.79% 22.19% 3.47% 4.16% 1.10% 0.90% 0.15% 0.59% 0.06% 0.20% 11 12 13 14 15 16 17 18 19 20 8 125 7 12 17 40 1 9 1 13 0.01% 0.19% 0.01% 0.02% 0.03% 0.06% 0.00% 0.01% 0.00% 0.02% 21 22 24 27 28 29 32 36 39 $$\mathrm{avg}\ 1.63$$ 5 2 10 2 2 1 2 1 1 66158 0.01% 0.00% 0.02% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00%