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 | $2^{6}\cdot4^{3}$ | ||
| 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
| $\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}15&70\\52&123\end{bmatrix}$, $\begin{bmatrix}39&62\\40&29\end{bmatrix}$, $\begin{bmatrix}45&38\\44&63\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 132.192.5.u.4 for the level structure with $-I$) |
| Cyclic 132-isogeny field degree: | $12$ |
| Cyclic 132-torsion field degree: | $480$ |
| Full 132-torsion field degree: | $158400$ |
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 | $12$ | $2$ | $2$ | $3$ | $0$ |
| 132.192.1-132.b.2.6 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.b.2.9 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.g.4.3 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.g.4.11 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.3.5 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.1-132.h.3.14 | $132$ | $2$ | $2$ | $1$ | $?$ |
| 132.192.3-132.f.1.3 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.f.1.12 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-12.g.2.8 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.u.2.5 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.u.2.6 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.v.2.5 | $132$ | $2$ | $2$ | $3$ | $?$ |
| 132.192.3-132.v.2.10 | $132$ | $2$ | $2$ | $3$ | $?$ |