Invariants
| Level: | $132$ | $\SL_2$-level: | $12$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot4^{2}\cdot6\cdot12^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12J0 |
Level structure
| $\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}13&74\\112&15\end{bmatrix}$, $\begin{bmatrix}60&83\\113&78\end{bmatrix}$, $\begin{bmatrix}63&122\\32&105\end{bmatrix}$, $\begin{bmatrix}97&54\\106&77\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 132.48.0.c.1 for the level structure with $-I$) |
| Cyclic 132-isogeny field degree: | $12$ |
| Cyclic 132-torsion field degree: | $480$ |
| Full 132-torsion field degree: | $633600$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 132.48.0-12.g.1.2 | $132$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.