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Is there a theorem which guarentees the existance of an elliptic curve with given number of points over $F_p$$\mathbf{F}_p$ for a given $p$.
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Is there a theorem which guarentees the existance of an elliptic curve with given number of points over $F_p$ for a given $p$.
Is there a theorem which guarentees the existance of an elliptic curve with given number of points over $\mathbf{F}_p$ for a given $p$.