What’s the exact definition of the alt_bn128 curve used by the Ethereum’s precompile?

Question

I just saw the following definition on neuromancer

But the the prime field don’t match the value’s used by Ethereum so there’re appears to be several curves using the same name…

But what’s the full parameters ? I’m meaning the other parameters that are $a$ ; $n$ and $G$ since it’s a Weirestrass curve…

Answer 1

EIP-196 Precompiled contracts for addition and scalar multiplication on the elliptic curve alt_bn128 specification says the curve is defined by:

Y^2 = X^3 + 3
over the field F_p with
p = 21888242871839275222246405745257275088696311157297823662689037894645226208583