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New Elliptic Curve Breaks 18-Year-Old Record | Quanta Magazine

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> Any one here know its rank?

My bad. The concept of rank does not really make sense in the context of curves over $$\mathbb{Q}$$.

> Instead, for elliptic curves over finite fields, we usually talk about the order or size of the group of points on the curve, not rank. For secp256k1, the order of the group of points is:

$$
n
=
115792089237316195423570985008687907852837564279074904382605163141518161494337
$$

> This number is prime, which means the elliptic curve secp256k1 is cyclic and has a single generator point (called G). Hence, every point on the curve can be written as a multiple of G.