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: | $\begin{bmatrix}15&58\\226&177\end{bmatrix}$, $\begin{bmatrix}81&118\\104&193\end{bmatrix}$, $\begin{bmatrix}123&152\\38&165\end{bmatrix}$, $\begin{bmatrix}165&122\\62&45\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.192.5.qg.3 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 no $\Q_p$ points for $p=23$, and therefore no 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.i.2.6 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 264.192.1-264.lk.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lk.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.3.6 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.lp.3.17 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.ls.3.3 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.1-264.ls.3.26 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.192.3-12.i.2.7 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dn.1.4 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.dn.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fl.1.1 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fl.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fo.2.10 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.192.3-264.fo.2.21 | $264$ | $2$ | $2$ | $3$ | $?$ |