论文标题
TATE正常形式的Hasse不变$ e_7 $和fricke group $γ_0^*（7）$的Supersingular多项式
The Hasse invariant of the Tate normal form $E_7$ and the supersingular polynomial for the Fricke group $Γ_0^*(7)$
论文作者
论文摘要
证明了一个公式，即在$ \ mathbb {f} _l $上超过$ \ mathbb {f} _l $的线性因素和不可约分因素的数量，hasse不变性$ \ hat h_ {7，l}（a）tate normal formal $ e_7（a）$ e_7（a）的订单$ 7 $，作为point $ 7 $的点数，作为一个unimalial $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ k = \ mathbb {q}（\ sqrt {-l}）$。指出了构想公式的$ \ h_ {7，l}（a）的二次和六因素的数量。与Fricke组$γ_0^*（7）$相对应的superingular多项式$ ss_l^{（7*）}（x）$。
A formula is proved for the number of linear factors and irreducible cubic factors over $\mathbb{F}_l$ of the Hasse invariant $\hat H_{7,l}(a)$ of the Tate normal form $E_7(a)$ for a point of order $7$, as a polynomial in the parameter $a$, in terms of the class number of the imaginary quadratic field $K=\mathbb{Q}(\sqrt{-l})$. Conjectural formulas are stated for the numbers of quadratic and sextic factors of $\hat H_{7,l}(a)$ of certain specific forms in terms of the class number of $\mathbb{Q}(\sqrt{-7l})$, which are shown to imply a recent conjecture of Nakaya on the number of linear factors over $\mathbb{F}_l$ of the supersingular polynomial $ss_l^{(7*)}(X)$ corresponding to the Fricke group $Γ_0^*(7)$.
