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 | $2^{2}\cdot4^{5}$ | ||
| 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: | $\begin{bmatrix}65&174\\90&17\end{bmatrix}$, $\begin{bmatrix}131&70\\204&259\end{bmatrix}$, $\begin{bmatrix}137&204\\174&155\end{bmatrix}$, $\begin{bmatrix}251&66\\98&151\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.5.qf.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| 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 |
|---|---|---|---|---|---|
| 24.192.3-24.cc.2.3 | $24$ | $2$ | $2$ | $3$ | $1$ |
| 132.192.1-132.g.4.11 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-132.g.4.4 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.ll.2.13 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.ll.2.27 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.1.5 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.1.31 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.3-24.cc.2.10 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dp.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dp.1.13 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fk.1.20 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fk.1.22 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fm.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fm.1.12 | $264$ | $2$ | $2$ | $3$ | $?$ |