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 | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24W7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}13&106\\244&65\end{bmatrix}$, $\begin{bmatrix}23&158\\200&145\end{bmatrix}$, $\begin{bmatrix}71&28\\76&25\end{bmatrix}$, $\begin{bmatrix}103&32\\204&89\end{bmatrix}$, $\begin{bmatrix}205&198\\44&23\end{bmatrix}$, $\begin{bmatrix}213&244\\8&201\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.144.7.bas.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 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.z.2.47 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 264.144.3-132.t.1.4 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.3-132.t.1.41 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.144.4-24.z.2.12 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.bm.1.30 | $264$ | $2$ | $2$ | $4$ | $?$ |
| 264.144.4-264.bm.1.48 | $264$ | $2$ | $2$ | $4$ | $?$ |