Invariants
| Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{6}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12E5 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}13&168\\0&1\end{bmatrix}$, $\begin{bmatrix}25&48\\12&193\end{bmatrix}$, $\begin{bmatrix}31&66\\168&181\end{bmatrix}$, $\begin{bmatrix}131&178\\80&81\end{bmatrix}$, $\begin{bmatrix}139&242\\96&167\end{bmatrix}$, $\begin{bmatrix}153&262\\68&253\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.5.on.3 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 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 |
|---|---|---|---|---|---|
| 12.192.3-12.g.2.5 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 264.192.1-264.lg.3.27 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lg.3.41 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lm.1.6 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lm.1.17 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.1.18 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.3-12.g.2.10 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.cu.1.41 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.cu.1.46 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fi.2.11 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fi.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fl.2.9 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fl.2.22 | $264$ | $2$ | $2$ | $3$ | $?$ |