Verifying the elliptic curve group law by strictly following its definition and performing the computation by hand was considered difficult. We show that a suitable change of variables makes such a manual calculation feasible. This method is rather uninstructive and offers no new insight, but we present it here in order to prevent others from wasting time on this tedious calculation. A more elegant method can be found in [1], and we recommend that busy readers consult that reference instead.
[1] Sander Zwegers. An elementary approach to the group law on elliptic curves. Arch. Math., 123(5):477–486, 2024.