The integral equation y² = x³ - x + 1 #
This file defines the integral Weierstrass equation, computes its discriminant -368, and
establishes ellipticity over ℚ and the normal form a₁ = a₃ = 0 there. It is the common
starting point for calculations of its rational torsion and Mordell–Weil rank.
@[reducible, inline]
The integral short equation y² = x³ - x + 1.
Instances For
The discriminant of y² = x³ - x + 1 is -368 = -16 * 23.
y² = x³ - x + 1 is an elliptic curve over ℚ.
Over ℚ, y² = x³ - x + 1 is in the normal form a₁ = a₃ = 0 of characteristic ≠ 2, the
form in which explicit 2-descent is set up.