Invariants
| Level: | $264$ | $\SL_2$-level: | $66$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $7 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot6\cdot22\cdot66$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 66B7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}2&87\\77&199\end{bmatrix}$, $\begin{bmatrix}41&198\\119&175\end{bmatrix}$, $\begin{bmatrix}42&157\\187&177\end{bmatrix}$, $\begin{bmatrix}53&162\\2&235\end{bmatrix}$, $\begin{bmatrix}227&253\\48&91\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 132.96.7.b.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $12$ |
| Cyclic 264-torsion field degree: | $960$ |
| Full 264-torsion field degree: | $5068800$ |
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 |
|---|---|---|---|---|---|
| $X_0(11)$ | $11$ | $16$ | $8$ | $1$ | $0$ |
| 24.16.0-12.b.1.3 | $24$ | $12$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.16.0-12.b.1.3 | $24$ | $12$ | $12$ | $0$ | $0$ |
| 264.96.3-33.a.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.96.3-33.a.1.31 | $264$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.384.13-132.g.1.6 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.g.2.6 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.g.3.3 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.g.4.3 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.h.1.6 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.h.2.6 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.h.3.3 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-132.h.4.3 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.cq.1.14 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.cq.2.14 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.cq.3.10 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.cq.4.10 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.ct.1.14 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.ct.2.14 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.ct.3.11 | $264$ | $2$ | $2$ | $13$ |
| 264.384.13-264.ct.4.11 | $264$ | $2$ | $2$ | $13$ |