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Dec 16, 2016 at 5:36 comment added Himanshu Shukla @FelipeVoloch can you please give me a link of the paper by Deuring
Dec 12, 2016 at 13:13 comment added Felipe Voloch @HimanshuShukla Deuring's proof developed into what's known as the CM method of constructing elliptic curves. I believe the construction is polynomial in $D{\log p}$ steps where $D = 4p - a^2$.
Dec 12, 2016 at 11:15 comment added znt That's a different question, and people are unlikely to spot it here as a comment on an answer. You should ask a different question.
Dec 12, 2016 at 9:02 comment added Himanshu Shukla Do we have any way to construct such an elliptic curve in polynomial in $logp$ steps or can anyone tell about algorithms on constructing them.
Dec 12, 2016 at 8:25 history answered Felipe Voloch CC BY-SA 3.0