Number Theory  ·  Research Tool

Which integers n
make this curve solvable?

y² = f(n, x)  —  find all integer (n, x, y)

The congruent number problem, Mordell curves, BSD conjecture — all reduce to asking when a parametric elliptic curve has integer points. This tool lets you define any such family, set your search range, and stream every solution directly to your browser in real time.

No installation. No account. Powered by NumPy, SymPy, and Server-Sent Events.

Open the solver View source on GitHub
01 / THE PROBLEM
Searching for integer points is computationally expensive

Naively testing every (n, x) pair over large ranges takes seconds per curve and is hard to parallelize on a laptop.

02 / THE APPROACH
Vectorised NumPy evaluation, streamed via SSE

The right-hand side is compiled once by SymPy, then evaluated over entire x-vectors in a single NumPy call per n — 100M+ evaluations per search.

03 / THE RESULT
Every integer triple (n, x, y) appears the moment it is found

Solutions stream to your browser live. LaTeX export, CSV download, and shareable URLs are included at no cost.

How it works

01
Define your curve

Enter any expression f(n, x) as the right-hand side of y² = … The tool supports polynomials, rational functions, and nested expressions.

02
Set your search bounds

Choose integer (or rational) ranges for n and x. Autoscale, fixed window, divisor-based, and expression-range x-modes are available.

03
Stream results in real time

A Server-Sent Events connection streams each triple (n, x, y) the instant it is discovered — no polling, no waiting for the full search to finish.

04
Export, share, and pin

Download as CSV or BibTeX, copy a shareable URL that encodes your exact search, or pin searches to your local history for later recall.