10 problems

Let $p\geq 5$ be a prime, and let … be a prime divisor of the order of the Monster group, with $N\neq 2,p$. Let $ss_p^{(N*)}(X)$ be the supersingular polynomial for the Fricke grou…

Let $l\neq 2,3,7$ be prime. Let $\hat H_{7,l}(x)$ be the Hasse-invariant polynomial of the Tate normal form $E_7$ over $\mathbb F_l$, and let $h(-l)$ be the relevant class number.…

Let $ss_p^{(7*)}(X)$ denote the supersingular polynomial for the Fricke group $\Gamma_0^*(7)$. Sakai--Nakaya's conjecture. The polynomial $ss_p^{(7*)}(X)$ is congruent modulo $p$ t…

Let $p$ be a prime, and let $ss_p^{(7*)}(X)$ denote the supersingular polynomial for the Fricke group $\Gamma_0^*(7)$. Let $\{A_n^{(N)}(X)\}_{n\geq 0}$ be the sequence of orthogona…

Class 3C supersingular-polynomial conjecture.

General-level degree formula conjecture.

General-level linear-factor formula conjecture.

Resultant multiplicity conjecture. The following congruences hold modulo $p$:

Sporadic-group linear-factor conjecture. For every prime $p$,

Heun polynomial representation conjecture. For every prime $p\geq7$,