I have an elliptic curve E1 which share an isogeny map with another elliptic curve E2 defined over the same finite field.
E1 is secure, it has a prime order which isn't equal to the prime field , large embedding degree, and is not pairing-friendly.
However, E2 shares the same properties, except that it's J-invariant and discriminant are totally different. the isogeny is of small degree.

Is it possible to leak any information about the ECDLP using operations between the curves in this case?

Whoever can come up with a working solution, I'm willing to pay upto $1000 for that.