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: | $20$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{2}\cdot12^{8}\cdot24^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AL7 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}33&104\\248&15\end{bmatrix}$, $\begin{bmatrix}91&252\\108&169\end{bmatrix}$, $\begin{bmatrix}177&40\\8&151\end{bmatrix}$, $\begin{bmatrix}187&162\\256&23\end{bmatrix}$, $\begin{bmatrix}199&96\\172&209\end{bmatrix}$, $\begin{bmatrix}227&70\\128&135\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.7.fv.2 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $24$ |
| Cyclic 264-torsion field degree: | $1920$ |
| Full 264-torsion field degree: | $2534400$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.47 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 264.192.3-132.l.2.55 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-132.l.2.63 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-24.bq.2.51 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dz.2.83 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dz.2.124 | $264$ | $2$ | $2$ | $3$ | $?$ |