A database of genus 2 curves over the rational numbers

Abstract

We describe the construction of a database of genus 2 curves of small discriminant that includes geometric and arithmetic invariants of each curve, its Jacobian, and the associated L-function. This data has been incorporated into the L-Functions and Modular Forms Database (LMFDB).

15 pages, 7 tables; bibliography formatting and typos fixed

References in corpus (8)

• Sato-Tate distributions and Galois endomorphism modules in genus 2
• Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time
• Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II
• Computing L-series of hyperelliptic curves
• Abelian surfaces of GL2-type as Jacobians of curves
• Computations on Modular Jacobian Surfaces
• Modular Curves Of Genus 2
• Computing $L$-functions and semistable reduction of superelliptic curves

Cited by in corpus (19)

• Rigorous computation of the endomorphism ring of a Jacobian
• Computing the geometric endomorphism ring of a genus 2 Jacobian
• Machine-Learning the Sato--Tate Conjecture
• A database of nonhyperelliptic genus 3 curves over Q
• A numerical transcendental method in algebraic geometry
• Computing L-series of geometrically hyperelliptic curves of genus three
• Bring's curve: Old and New
• Numerical computation of endomorphism rings
• Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over $\mathbb{Q}$ up to squares
• Explicit two-cover descent for genus 2 curves
• A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line
• Effective homology and periods of complex projective hypersurfaces
• 3-torsion and conductor of genus 2 curves
• Divisibility of torsion subgroups of abelian surfaces over number fields
• A geometric linear Chabauty comparison theorem
• Endomorphism algebras of abelian varieties with large cyclic 2-torsion field over a given field
• Evaluating modular equations for abelian surfaces
• Computing Euler factors of genus 2 curves at odd primes of almost good reduction
• Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields