PARI includes (among many other things) an implementation of Schoof's algorithm (more specifically the Schoof-Elkies-Atkin algorithm).
? p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
%1 = 115792089237316195423570985008687907853269984665640564039457584007908834671663
? ellcard(ellinit([0,7], p))
%2 = 115792089237316195423570985008687907852837564279074904382605163141518161494337
It's open source, so you can easily look inside.
If you don't want to install PARI, CoCalc lets you run PARI (or Sage) in a browser. Just start up a new project, and inside that a new Linux terminal, enter "gp" and you're off and running in PARI.
Alternatively you can do the computation directly in Sage (which you can also run via CoCalc: New → Sage worksheet), but this doesn't give you any new implementation since Sage just calls PARI for this function:
sage: p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
sage: EllipticCurve(GF(p), [0,7]).order()
115792089237316195423570985008687907852837564279074904382605163141518161494337
For documentation in PARI:
? ?ellcard
ellcard(E,{p}): given an elliptic curve E defined over a finite field Fq,
return the order of the group E(Fq); for other fields of definition K, p must
define a finite residue field, (p prime for K = Qp or Q; p a maximal ideal for
K a number field), return the order of the (non-singular) reduction of E.
For documentation in Sage:
sage: E = EllipticCurve(GF(p), [0,7])
sage: E.order?
sage: E.order??