<p>Over the field <em>GF(2<sup>256</sup> - 2<sup>32</sup> - 977)</em>, the equation <em>y<sup>2</sup> = x<sup>3</sup> + 7</em> has exactly</p>
<p>115792089237316195423570985008687907852837564279074904382605163141518161494336</p>
<p>distinct solutions for <em>(x, y)</em>, or roughly <em>2<sup>256</sup> - 1.27077×2<sup>128</sup></em>. Together with the point at infinity (which is part of the group, but not the curve), the group size is one more than that. Since that yields a prime number, the group is cyclic (all prime-sized groups are), and only has itself and the trivial group (just the point at infinity) as subgroups.</p>

CC BY-SA 4.0
2022-10-21T16:18:49.067Z
Thanks! Must have been looking at subgroups for a different curve.
kuco 23
CC BY-SA 4.0
2022-10-21T13:32:52.233Z
2022-10-22T03:14:19.407Z
2022-10-22T03:14:19.407Z
Pieter Wuille
<p>I'm wondering whether it is known how many elements does Bitcoin's elliptic curve have? Have not been able to find an answer to this, only for specific subgroups.</p>

<secp256k1>
How many elements does Bitcoin's secp256k1 have?
kuco 23
# How many elements does Bitcoin's secp256k1 have?

(Asked by: username_0 on 2022-10-21)

I'm wondering whether it is known how many elements does Bitcoin's elliptic curve have? Have not been able to find an answer to this, only for specific subgroups.

**Tags:** secp256k1


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## 1 answers

### Answer by username_1 on 2022-10-21. Score: 6 | Accepted answer

Over the field *GF(2256 - 232 - 977)*, the equation *y2 = x3 + 7* has exactly

115792089237316195423570985008687907852837564279074904382605163141518161494336

distinct solutions for *(x, y)*, or roughly *2256 - 1.27077×2128*. Together with the point at infinity (which is part of the group, but not the curve), the group size is one more than that. Since that yields a prime number, the group is cyclic (all prime-sized groups are), and only has itself and the trivial group (just the point at infinity) as subgroups.

> **Comments:**
> **username_0**: Thanks! Must have been looking at subgroups for a different curve.  

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