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.
1 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.
answered Oct 21, 2022 at 13:32
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Thanks! Must have been looking at subgroups for a different curve.– kuco 23Commented Oct 21, 2022 at 16:18