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

Distribution of num rat pts

num rat pts 0 0 1 1 2 2 3 3 4 4
count 5140 5140 6454 6454 11575 11575 8719 8719 9434 9434
proportion 7.77% 7.77% 9.76% 9.76% 17.50% 17.50% 13.18% 13.18% 14.26% 14.26%
num rat pts 5 5 6 6 7 7 8 8 9 9
count 5089 5089 6561 6561 2967 2967 3911 3911 1328 1328
proportion 7.69% 7.69% 9.92% 9.92% 4.48% 4.48% 5.91% 5.91% 2.01% 2.01%
num rat pts 10 10 11 12 12 13 14 15 16 17
count 1926 1926 578 1130 1130 234 574 97 276 28
proportion 2.91% 2.91% 0.87% 1.71% 1.71% 0.35% 0.87% 0.15% 0.42% 0.04%
num rat pts 18 19 20 21 22 24 26 1- \(\mathrm{avg}\ 4.25\)
count 103 2 20 1 3 6 2 61018 66158
proportion 0.16% 0.00% 0.03% 0.00% 0.00% 0.01% 0.00% 92.23% 100.00%

Distribution of rational Weierstrass points

num rat wpts 0 0 1 1 2 2 3 4 \(\mathrm{avg}\ 0.66\)
count 32616 32616 24611 24611 8005 8005 886 40 66158
proportion 49.30% 49.30% 37.20% 37.20% 12.10% 12.10% 1.34% 0.06% 100.00%

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

aut grp id \(D_6\) \(C_2\) \(C_2\) \(C_4\) \(V_4\) \(V_4\) \(C_6\) \(D_4\)
count 4 63480 63480 15 2597 2597 58 4
proportion 0.01% 95.95% 95.95% 0.02% 3.93% 3.93% 0.09% 0.01%

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

geom aut grp id \(C_{10}\) \(D_6\) \(C_2\) \(C_2\) \(2D_6\) \(V_4\) \(V_4\) \(\tilde{S}_4\) \(D_4\)
count 5 88 63310 63310 4 2698 2698 3 50
proportion 0.01% 0.13% 95.70% 95.70% 0.01% 4.08% 4.08% 0.00% 0.08%

Distribution of analytic ranks

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

Distribution of two selmer ranks

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

Distribution of squareness of Ш

has square sha False False True True
count 2284 2284 63874 63874
proportion 3.45% 3.45% 96.55% 96.55%

Distribution of local solvability

locally solvable False False True True
count 3371 3371 62787 62787
proportion 5.10% 5.10% 94.90% 94.90%

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

is gl2 type False False True True
count 63312 63312 2846 2846
proportion 95.70% 95.70% 4.30% 4.30%

Distribution of Sato-Tate group identity components

real geom end alg \(\mathrm{U}(1)\times\mathrm{U}(1)\) \(\mathrm{U}(1)\times\mathrm{SU}(2)\) \(\mathrm{U}(1)\) \(\mathrm{SU}(2)\) \(\mathrm{USp}(4)\) \(\mathrm{USp}(4)\) \(\mathrm{SU}(2)\times\mathrm{SU}(2)\) \(\mathrm{SU}(2)\times\mathrm{SU}(2)\)
count 6 303 8 150 63107 63107 2584 2584
proportion 0.01% 0.46% 0.01% 0.23% 95.39% 95.39% 3.91% 3.91%

Distribution of st groups

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

Distribution of torsion subgroup orders

torsion order 1 1 2 2 3 3 4 4 5 6
count 44190 44190 14681 14681 2295 2295 2754 2754 725 595
proportion 66.79% 66.79% 22.19% 22.19% 3.47% 3.47% 4.16% 4.16% 1.10% 0.90%
torsion order 7 8 9 10 11 12 13 14 15 16
count 97 393 38 131 8 125 7 12 17 40
proportion 0.15% 0.59% 0.06% 0.20% 0.01% 0.19% 0.01% 0.02% 0.03% 0.06%
torsion order 17 18 19 20 21 22 24 27 28 29
count 1 9 1 13 5 2 10 2 2 1
proportion 0.00% 0.01% 0.00% 0.02% 0.01% 0.00% 0.02% 0.00% 0.00% 0.00%
torsion order 32 36 39 5- \(\mathrm{avg}\ 1.63\)
count 2 1 1 2238 66158
proportion 0.00% 0.00% 0.00% 3.38% 100.00%