Number Theory · Research Tool
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.
Naively testing every (n, x) pair over large ranges takes seconds per curve and is hard to parallelize on a laptop.
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.
Solutions stream to your browser live. LaTeX export, CSV download, and shareable URLs are included at no cost.
How it works
Enter any expression f(n, x) as the right-hand side of y² = …
The tool supports polynomials, rational functions, and nested expressions.
Choose integer (or rational) ranges for n and x. Autoscale, fixed window, divisor-based, and expression-range x-modes are available.
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.
Download as CSV or BibTeX, copy a shareable URL that encodes your exact search, or pin searches to your local history for later recall.