Invariants
| Level: | $168$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
| Index: | $336$ | $\PSL_2$-index: | $336$ | ||||
| Genus: | $21 = 1 + \frac{ 336 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $7^{8}\cdot14^{4}\cdot56^{4}$ | Cusp orbits | $1^{2}\cdot2\cdot3^{2}\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 21$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 21$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 56F21 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}18&167\\31&150\end{bmatrix}$, $\begin{bmatrix}28&37\\19&114\end{bmatrix}$, $\begin{bmatrix}35&132\\50&125\end{bmatrix}$, $\begin{bmatrix}48&127\\7&8\end{bmatrix}$, $\begin{bmatrix}79&68\\86&21\end{bmatrix}$, $\begin{bmatrix}108&37\\131&138\end{bmatrix}$, $\begin{bmatrix}150&113\\53&158\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 168-isogeny field degree: | $16$ |
| Cyclic 168-torsion field degree: | $768$ |
| Full 168-torsion field degree: | $442368$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 28.168.9.c.1 | $28$ | $2$ | $2$ | $9$ | $0$ |
| 168.12.0.bb.1 | $168$ | $28$ | $28$ | $0$ | $?$ |