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TauCeti.AlgebraicGeometry.EllipticCurve.MordellWeil.WorkedExamples.X3SubXAddOne.Basic

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.

    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.