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The LMFDB universe
Introduction
Overview
Random
Universe
Knowledge
L-functions
Degree 1
Degree 2
Degree 3
Degree 4
$\zeta$ zeros
Modular forms
Classical
Maass
Hilbert
Bianchi
Varieties
Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Fields
Number fields
$p$-adic fields
Representations
Dirichlet characters
Artin representations
Groups
Galois groups
Sato-Tate groups
The top half of the diagram is based on the
Langlands program
, which predicts that any motivic object corresponds to an automorphic object via their L-functions.