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The database currently contains 66,158 genus 2 curves over $\Q$ of absolute discriminant up to 1,000,000. Here are some further statistics.

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By conductor: 1-499   500-999   1000-9999   10000-99999   100000-1000000  
By absolute discriminant: 1-499   500-999   1000-9999   10000-99999   100000-1000000  
By $\overline{\Q}$-automorphism group: $C_2$   $C_2^2$   $D_4$   $C_{10}$   $D_6$   $C_3:D_4$   $\mathrm{GL}(2,3)$
Some interesting genus 2 curves or a random genus 2 curve

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\(\overline{\Q}\)-invariants
Bad primes e.g. 2 or 2,3,5 Geometrically simple
Conductor e.g. 169, 100-1000 $\GL_2$-type
Absolute discriminant e.g. 169, 0-1000 Sato-Tate group
Rational points* e.g. 0, 20-26 Sate-Tate identity component
Rational Weierstrass points e.g. 1, 0-6 \(\Q\)-automorphism group
Torsion order e.g. 2 \(\overline{\Q}\)-automorphism group
Torsion structure e.g. [2,2,2] \(\Q\)-endomorphism algebra
2-Selmer rank e.g. 1 \(\overline{\Q}\)-endomorphism algebra
Analytic order of Ш* e.g. 2 Order of Ш is square*
Analytic rank* e.g. 1 Locally solvable
Galois image e.g. 2.45.1 or 3.720.4 Nonmaximal $\ell$ e.g. 2,3
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  *Items marked with an asterisk are only known conditionally (click captions for details). Searches will match conditional values.

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Label or polynomial
e.g. 169.a.169.1 or 169.a or 1088.b or x^5 + 1 or x^5, x^2 + x + 1 or b^2 = k^5 + 1 or m^2 + m*(x^2 + x + 1) = x^5