Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $8^{16}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16B7 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}17&152\\0&53\end{bmatrix}$, $\begin{bmatrix}57&16\\148&47\end{bmatrix}$, $\begin{bmatrix}137&148\\104&89\end{bmatrix}$, $\begin{bmatrix}145&96\\32&151\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.192.7.k.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $48$ |
| Cyclic 176-torsion field degree: | $960$ |
| Full 176-torsion field degree: | $844800$ |
Rational points
This modular curve has no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.2-16.a.1.2 | $16$ | $2$ | $2$ | $2$ | $0$ |
| 88.192.3-88.x.1.1 | $88$ | $2$ | $2$ | $3$ | $?$ |
| 176.192.2-16.a.1.16 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.192.2-176.c.1.1 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.192.2-176.c.1.31 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.192.3-88.x.1.2 | $176$ | $2$ | $2$ | $3$ | $?$ |