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On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
On Orders Of Elliptic Curves Over Finite Fields, Yujin H. Kim, Jackson Bahr, Eric Neyman, Gregory Taylor
Rose-Hulman Undergraduate Mathematics Journal
In this work, we completely characterize by $j$-invariant the number of orders of elliptic curves over all finite fields $F_{p^r}$ using combinatorial arguments and elementary number theory. Whenever possible, we state and prove exactly which orders can be taken on.