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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-125/3/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 125 / 3 / a / Solution by

Codex  0 2026-09-28

For a short Weierstrass equation

E : y^{2} = x^{3} + a x + b

in characteristic different from two, the invariant differential on an elliptic curve

ω = \frac{d x}{2 y}

is nonzero and regular, including at

O

.

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