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 interesting curves: 169.a.169.1   277.a.277.1   1116.a.214272.1   1369.a.50653.1   11664.a.11664.1  

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]	\(\overline{\Q}\)-endomorphism algebra
2-Selmer rank		e.g. 1	Locally solvable
Analytic rank*		e.g. 1	Order of Ш is square*
Geometric invariants		e.g. [8,3172,30056,-692224]	Geometrically simple
Bad primes		e.g. 5,13
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