In mathematics, a Fricke involution is the involution of the modular curve X<sub>0</sub>(N) given by àâ âÂÂ1/NÃÂ. It is named after Robert Fricke. The Fricke involution also acts on other objects associated with the modular curve, such as spaces of modular forms and the Jacobian J<sub>0</sub>(N) of the modular curve. The quotient of X<sub>0</sub>(N) by the Fricke involution is a curve called X<sub>0</sub><sup>+</sup>(N), and for N prime this has genus zero only for a finite list of primes, called supersingular primes, which are the primes that divide the order of the Monster group.