y^{2} = x^{3} + ax + b

disc(E) = −16(4a^{3} + 27b^{2}) ≠ 0

E(Q) = {(x, y) ∈ Q × Q : y^{2} = x^{3} + ax + b} ∪ {∞}

Gal(\overline{Q}/Q)