An online elliptic curve calculator that computes exactly - using BigInt throughout - point addition, doubling, scalar multiplication (double-and-add), negation and curve order on y² = x³ + ax + b (mod p).

The input format follows the input mode: in point mode write x,y per line; in point-pair mode write x1,y1; x2,y2; in scalar mode write k; x,y. Curve parameters can be typed in manually (decimal or 0x hex) or picked from presets such as secp256k1 and P-256.

When P = Q the addition falls back to point doubling, and when P = -Q the result is the identity element O (point at infinity); for doubling, y = 0 gives 2P = O. Every point is validated to be on the curve, the discriminant is used to check that the curve is non-singular (a singular curve is reported as not a valid elliptic curve), and for p ≤ 100000 the curve order n and the order of each point are counted by enumeration.

Note: this tool is for teaching and demonstration, is not a cryptographically secure implementation (no constant time, no side-channel protection) and must not be used to generate production keys.