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Elliptic Curve Solver

Search for rational n where y² = f(n, x) has integer points

Number Theory Tool

Find where  y² = f(n, x)
has integer points

Define any parametric elliptic curve family, set your search range, and watch integer solutions stream to your browser in real time — powered by NumPy, SymPy, and Server-Sent Events.

▶  Start Exploring How it works
23+digit n values
100M+evaluations / search
Real-timestreaming results
LaTeXequation import
Enter a curve expression and click Run Search.

How It Works

1

Parse the curve

Your expression is parsed by SymPy into a symbolic form and compiled to a fast numeric function.

2

Iterate over (n, x)

For each rational value of n in your range, every integer x is tested. The server computes f(n, x) and checks whether it is a perfect square.

3

Emit integer points

Whenever f(n, x) is a non-negative perfect square, the triple (n, x, ±y) is streamed to your browser in real time.

4

Export results

All discovered integer points can be downloaded as a CSV file for further analysis or verification.

Mathematical context

An elliptic curve over ℚ can be written in Weierstrass form as y² = x³ + ax + b. By introducing a rational parameter n, families of curves such as y² = x³ − n²x arise naturally (this is the congruent number curve). This tool lets you specify any such family and exhaustively search for integer points — useful for number-theory experiments and Diophantine equation research.

Example Curves