I believe you are thinking of "Supersingular isogeny Diffie–Hellman key exchange" or SIKE which is a post quantum encryption algorithm that was spectacularly broken a couple years ago. The math involves elliptical curves but it's different from the elliptical curve cryptography used in your browser.
Which assumptions? ECDLP is still considered computationally hard, and ECC considered secure. There are invalid curve attacks and small subgroup attacks but that's a problem with key selection, not a fundamental problem with ECC.
Do you have a citation?
Could you link to any more information about this?
Not in general, no. It is still secure and used. There are of course attacks but those were not completely breaking