Invariants
| Level: | $132$ | $\SL_2$-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
| $\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}39&10\\98&73\end{bmatrix}$, $\begin{bmatrix}83&10\\80&45\end{bmatrix}$, $\begin{bmatrix}97&14\\102&71\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 132.192.5.t.2 for the level structure with $-I$) |
| Cyclic 132-isogeny field degree: | $24$ |
| Cyclic 132-torsion field degree: | $480$ |
| Full 132-torsion field degree: | $158400$ |
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.f.1.2 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 132.192.1-132.a.2.3 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.a.2.12 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.2.6 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.2.11 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.3.5 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.3.11 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.3-132.e.1.5 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.e.1.11 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-12.f.1.8 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.v.2.7 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.v.2.10 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.v.2.11 | $132$ | $2$ | $2$ | $3$ | $?$ |