If we have addition, then it does follow to say that, by the definition of the words and the operations, there is subtraction, multiplication and division. But to be redundant, they cannot be applied directly to points on the curve, but to their constituent parts to produce the result desired.
When it comes to addition and subtraction, then you can apply that to any two public keys. However, if you have multiplication and division, then you can only multiply or divide a public key by a private key. You cannot divide or multiply two public keys alone, here is why:
https://bitcointalk.org/index.php?topic=5460766.0So, I guess the way forward for you, would be to test everything on a small elliptic curve, where you can brute force everything. And then, switch to a little bit bigger one. And so on, and so forth. Example parameters:
https://bitcointalk.org/index.php?topic=5459153.0