Supersingular prime (moonshine theory)

In the

The non-supersingular primes are 37, 43, 53, 61, 67, and any prime number greater than or equal to 73.

Supersingular primes are related to the notion of supersingular elliptic curves as follows. For a prime number p, the following are equivalent:

1. The modular curve X₀⁺(p) = X₀(p) / w_p, where w_p is the Fricke involution of X₀(p), has genus zero.
2. Every supersingular elliptic curve in characteristic p can be defined over the
   prime subfield
   F_p.
3. The order of the Monster group is divisible by p.

The equivalence is due to

All supersingular primes are Chen primes, but 37, 53, and 67 are also Chen primes, and there are infinitely many Chen primes greater than 73.

• Supersingular prime (algebraic number theory)

• Weisstein, Eric W. "Supersingular Prime". MathWorld.
• Weisstein, Eric W. "Sporadic group". MathWorld.
• MR 0604631
  .