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Old 2021-01-29, 22:29   #7
Robert Holmes
 
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Oct 2007

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The key term here is supersingular elliptic curves. For p = 2 mod 3, any curve of the form y^2 = x^3 + B is supersingular, p > 3.

Another common case is p = 3 mod 4, in which case y^2 = x^3 + x is also known to be supersingular.
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