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 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.

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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	Sato-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]	locally solvable
2-Selmer rank		e.g. 1	order of Ш is square*
analytic rank*		e.g. 1	geometrically simple
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