Get a half point of a point on elliptic curve.

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Yos
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Let $E$ be an elliptic cuve on finite field, $P\in E$ be a rational point. Then, I want to get one of point $Q\in E$ such that $2Q=P$ .

What shoud I do?

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Find the order $N$ of $E$ and compute $\frac{N+1}2P$ ?

Max Alekseyev ( 1 year ago )

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Luca
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The method P.division_points(n) gives the list of all rational points Q such that nQ = P. It works for any base field.

sage: E = EllipticCurve([1,0])
sage: P = E(0)
sage: P.division_points(2)
[(0 : 0 : 1), (0 : 1 : 0)]

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Asked: 1 year ago

Seen: 281 times

Last updated: Feb 04 '24