Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}\cdot12^{4}\cdot24^{4}$ | Cusp orbits | $1^{4}\cdot2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AH9 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}7&216\\244&179\end{bmatrix}$, $\begin{bmatrix}21&124\\256&177\end{bmatrix}$, $\begin{bmatrix}25&254\\244&219\end{bmatrix}$, $\begin{bmatrix}173&40\\120&163\end{bmatrix}$, $\begin{bmatrix}181&158\\4&105\end{bmatrix}$, $\begin{bmatrix}209&112\\24&139\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.9.jl.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
| 88.96.1-88.bf.2.4 | $88$ | $4$ | $4$ | $1$ | $?$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.47 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 88.96.1-88.bf.2.4 | $88$ | $4$ | $4$ | $1$ | $?$ |
| 264.192.3-24.bq.2.7 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dy.1.1 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dy.1.116 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.5-264.c.1.15 | $264$ | $2$ | $2$ | $5$ | $?$ |
| 264.192.5-264.c.1.63 | $264$ | $2$ | $2$ | $5$ | $?$ |