##  [Anomalous Prime](/anomalous-prime) 

  ##  [Anomalous Prime](https://puremath.quantumdictionary.io/anomalous-prime-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For an elliptic curve E over Q (or a number field), a prime p of good reduction is called anomalous if the number of F_p-points satisfies #E(F_p) ≡ 1 (mod p), equivalently the trace of Frobenius a_p satisfies a_p ≡ 0 (mod p), yielding exceptional arithmetic and algorithmic behavior.