> 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.

south_korea_ln

science

> The curve’s equation, when written as $$y^2 = x^3 + Ax + B$$, has values of A and B that are each over 60 digits long. The 29 independent rational solutions that Elkies and Klagsbrun pinpointed involve numbers that are similarly huge.

In bitcoin, we use secp256k1 with
$$
y^2= x^3+7.
$$
Any one here know its rank?