Please support the section 7 of this paper for attacking anomalous curves.

[ytrezq]

I know you already supports attacking anomalous curves, but I found this paper https://sciencedirect.com/science/article/pii/S0022314X08000486 that provide a far better method if it could be extended to other curves (not just anomalous ones).

Unlike other methods, the lift must be non canonical and the dependancy (that is, the discrete logarithm) must be broken. Other methods requires the listed points to be dependant.