Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $12^{8}\cdot24^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24J8 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}73&204\\96&223\end{bmatrix}$, $\begin{bmatrix}141&202\\188&129\end{bmatrix}$, $\begin{bmatrix}145&248\\80&71\end{bmatrix}$, $\begin{bmatrix}155&76\\100&145\end{bmatrix}$, $\begin{bmatrix}225&230\\116&87\end{bmatrix}$, $\begin{bmatrix}239&96\\36&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.144.8.iy.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $7680$ |
| Full 264-torsion field degree: | $3379200$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.4-24.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 264.144.4-132.m.1.13 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-132.m.1.53 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-24.z.2.61 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.bm.1.43 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.bm.1.100 | $264$ | $2$ | $2$ | $4$ | $?$ |