Invariants
| Level: | $132$ | $\SL_2$-level: | $132$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $19 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (all of which are rational) | Cusp widths | $1^{2}\cdot3^{2}\cdot4\cdot11^{2}\cdot12\cdot33^{2}\cdot44\cdot132$ | Cusp orbits | $1^{12}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 19$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 19$ | ||||||
| Rational cusps: | $12$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 132D19 |
Level structure
| $\GL_2(\Z/132\Z)$-generators: | $\begin{bmatrix}25&115\\0&107\end{bmatrix}$, $\begin{bmatrix}37&18\\0&7\end{bmatrix}$, $\begin{bmatrix}41&110\\0&47\end{bmatrix}$, $\begin{bmatrix}65&45\\0&5\end{bmatrix}$, $\begin{bmatrix}95&8\\0&19\end{bmatrix}$, $\begin{bmatrix}125&4\\0&13\end{bmatrix}$, $\begin{bmatrix}125&56\\0&43\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 132-isogeny field degree: | $1$ |
| Cyclic 132-torsion field degree: | $40$ |
| Full 132-torsion field degree: | $211200$ |
Rational points
This modular curve has 12 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(3)$ | $3$ | $72$ | $72$ | $0$ | $0$ |
| $X_0(4)$ | $4$ | $48$ | $48$ | $0$ | $0$ |
| $X_0(11)$ | $11$ | $24$ | $24$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(12)$ | $12$ | $12$ | $12$ | $0$ | $0$ |
| $X_0(44)$ | $44$ | $4$ | $4$ | $4$ | $0$ |
| $X_0(66)$ | $66$ | $2$ | $2$ | $9$ | $0$ |