Is there a quick math trick to determine if two points share the same higher level endomorphic ring? Just by their X and Y?
By higher-level, I mean 149 or 631. 2 and 3 are obvious. I know that all of the points that share the same subgroup sum up to O. It's also possible to build up the subgroup entirely, but is this really required, in order to make such a check, that the other point is in the same subgroup?
If I understood your question right, maybe one possible way to simplify the check is to first verify whether both points are n-torsion points (nP = O and nQ = O). If not, you can already rule out that they belong to the same n-order subgroup. If they both are, i think you have to build up the entire subgroup as you said, i don't think there is a direct way to check. But at least the n-torsion check can help "quickly" exclude cases that definitely don’t match, or at least use less computation. Could this make sense?