Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| 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: | 24AI7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}1&20\\96&185\end{bmatrix}$, $\begin{bmatrix}121&180\\64&5\end{bmatrix}$, $\begin{bmatrix}131&172\\72&169\end{bmatrix}$, $\begin{bmatrix}199&257\\40&93\end{bmatrix}$, $\begin{bmatrix}233&234\\216&257\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.7.lf.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $12$ |
| Cyclic 264-torsion field degree: | $480$ |
| Full 264-torsion field degree: | $2534400$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=7$, and therefore no 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 |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
| 88.96.0-88.bi.1.2 | $88$ | $4$ | $4$ | $0$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.gf.2.3 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 88.96.0-88.bi.1.2 | $88$ | $4$ | $4$ | $0$ | $?$ |
| 264.192.3-24.gf.2.17 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.lr.1.30 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.lr.1.41 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pk.2.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.pk.2.51 | $264$ | $2$ | $2$ | $3$ | $?$ |