Abstract
A proof is given of several conjectures from a recent paper of Nakaya concerning the supersingular polynomial [Formula: see text] for the Fricke group [Formula: see text], for [Formula: see text]. One of these conjectures gives a formula for the square of [Formula: see text] (mod [Formula: see text]) in terms of a certain resultant, and the other relates the primes [Formula: see text] for which [Formula: see text] splits into linear factors (mod [Formula: see text]) to the orders of certain sporadic simple groups.
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