Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{8}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24J7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}11&6\\16&97\end{bmatrix}$, $\begin{bmatrix}49&6\\120&205\end{bmatrix}$, $\begin{bmatrix}161&0\\88&97\end{bmatrix}$, $\begin{bmatrix}181&230\\32&209\end{bmatrix}$, $\begin{bmatrix}195&44\\56&25\end{bmatrix}$, $\begin{bmatrix}241&136\\88&153\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.144.7.bjg.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $3379200$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 264.144.3-264.bh.1.39 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-264.bh.1.42 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-264.byt.1.18 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-264.byt.1.40 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-264.caw.1.9 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-264.caw.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.4-264.bd.1.18 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.bd.1.77 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-24.ch.1.26 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.qj.1.17 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.qj.1.40 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.sa.1.9 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.sa.1.24 | $264$ | $2$ | $2$ | $4$ | $?$ |