Math
Elliptic curves
Visualize the elliptic-curve group law with real chords and tangents, and calculate exact point sums in small prime fields.
Try this
Explore chord-and-tangent addition over the reals or exact modular addition over a prime field. Finite-field buttons select points; ∞ is the group identity. Singular curves are excluded.
Equations used in the module
Equations y² = x³ + ax + b; Δ = −16(4a³ + 27b²) ≠ 0 m = (yQ−yP)/(xQ−xP); tangent m = (3xP²+a)/(2yP) xR = m²−xP−xQ; yR = m(xP−xR)−yP Over Fp, division uses the modular inverse; P + (−P) = ∞
