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$j$-invariants of elliptic curves over finite fields

It is in general $\textit{not}$ true that $\textit{if}$ $A$ and $B$ are elliptic curves over the finite field $K$, lying in the same $K$-isogeny class, and with the same $j$-invariant, $\textit{then}$ …
Tommaso Centeleghe's user avatar