Invariants
| Level: | $264$ | $\SL_2$-level: | $44$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot22^{2}\cdot44^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 44B9 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}19&110\\20&47\end{bmatrix}$, $\begin{bmatrix}31&66\\84&257\end{bmatrix}$, $\begin{bmatrix}85&198\\222&23\end{bmatrix}$, $\begin{bmatrix}97&66\\216&31\end{bmatrix}$, $\begin{bmatrix}139&0\\200&241\end{bmatrix}$, $\begin{bmatrix}195&22\\130&75\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.144.9.b.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $16$ |
| Cyclic 264-torsion field degree: | $1280$ |
| Full 264-torsion field degree: | $3379200$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(11)$ | $11$ | $24$ | $12$ | $1$ | $0$ |
| 24.24.0-8.b.1.4 | $24$ | $12$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.0-8.b.1.4 | $24$ | $12$ | $12$ | $0$ | $0$ |
| 132.144.4-22.a.1.10 | $132$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-22.a.1.4 | $264$ | $2$ | $2$ | $4$ | $?$ |