Is it possible to solve the ECDLP in this situation?

[bitcoinend]

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.

[ThewsyRum]

This is impossible. An isogeny between prime-order curves requires a trivial kernel or a kernel of size equal to the prime order, which would collapse the curve into a trivial group. E1 and E2 have distinct J-invariants, so no non-trivial isogeny can exist. It is mathematically impossible

[bitcoinend]

This is impossible. An isogeny between prime-order curves requires a trivial kernel or a kernel of size equal to the prime order, which would collapse the curve into a trivial group. E1 and E2 have distinct J-invariants, so no non-trivial isogeny can exist. It is mathematically impossible

Do you mean no such isogeny can exist?
That's incorrect.
No such isomorphism (which can be thought of as isogeny of 1 degree) can exist. but isogeny of other prime degrees can exist having different j-invariants.