LMFDB - The L-functions and modular forms database

Overview

Curated map of the LMFDB (L-functions and Modular Forms Database) by mathematical area — ALWAYS CALL THIS FIRST for any task involving number theory data. Covers these mathematical areas: elliptic curves over Q and over number fields, classical modular forms, Maass forms, Hilbert modular forms, Bianchi modular forms, genus 2 curves, higher genus families, L-functions, number fields, p-adic fields, Dirichlet characters, Artin representations, Galois groups, Sato-T

List Tables

List LMFDB tables with metadata (section, notes) when available. If you're starting a new task, prefer overview() — it gives the same metadata grouped by mathematical area and is usually more useful. Use list_tables when you need a flat list or when filtering by a prefix you already know. By default returns only production tables flagged visible through the MCP (status='production', mcp_visible=true in the lmfdb_tables metadata). Pass status='all' to also include ta

Search Knowls

Search LMFDB documentation for tables and columns matching the given keywords. Use this to discover which table or column contains a mathematical quantity you're looking for. This is typically the first tool to call when you know what mathematical data you want but don't know where it's stored. For example: - search_knowls("frobenius traces") finds columns storing a_p values - search_knowls("isogeny class") finds tables about isogeny classes - search_knowls

Describe Table

Show the column names, types, and (where available) documentation for a given LMFDB table. The output includes: - table_name - description: the contents of the knowl "tables.<table_name>", if any, describing what the table represents - columns: a list of {column_name, data_type, is_nullable, description, array_length} objects. "description" comes from the knowl "columns.<table_name>.<column_name>", if any. "array_length" is present for a

Sample Rows

Return a random sample of rows from a table to understand its contents. Args: table_name: The table to sample (e.g. "ec_curvedata"). n: Number of rows to return (default 5, max 50). Returns: JSON with columns and sample rows.

Run Sql

Run a read-only SQL SELECT query against the LMFDB database. This is the most flexible tool — use it for filtering, joining, aggregating, or computing statistics across LMFDB tables. Args: sql: A SELECT query. Only SELECT/WITH/EXPLAIN statements are allowed. Examples: - SELECT label, rank, conductor FROM ec_curvedata WHERE rank >= 3 LIMIT 20 - SELECT st_group, COUNT(*) FROM g2c_curves GROUP BY st_group - SELECT AVG(r

Count Rows

Count rows in a table, optionally with a WHERE clause. Args: table_name: The table to count (e.g. "ec_curvedata"). where: Optional WHERE clause without the WHERE keyword (e.g. "rank >= 2 AND conductor < 1000"). Returns: JSON with the count.

Table Stats

Compute basic statistics for a numeric column in a table. For non-numeric columns, returns count and distinct count only. Args: table_name: The table (e.g. "ec_curvedata"). column: The column to analyze (e.g. "rank", "conductor"). where: Optional WHERE clause without the keyword. Returns: JSON with count, distinct_count, and (for numeric columns) min, max, avg, stddev.

Export Query

Prepare a bulk download of a SELECT query's results. Returns a short- lived URL that streams the full result set as CSV or JSONL — the data does NOT go through the MCP conversation, so this is the right tool for anything destined for client-side analysis (pandas, numpy, plots, machine learning, etc.) rather than direct inspection. Typical use: ask the LLM to write a query joining several tables and selecting the columns you want, call export_query, then in the LLM's