Genus 2 curves over $\Q$

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

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

Search

\(\overline{\Q}\)-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
Results to display

Display:

  *Items marked with an asterisk are only known conditionally (click captions for details). Searches will match conditional values.

Find

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