Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | 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: | $24$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16O5 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}59&12\\64&17\end{bmatrix}$, $\begin{bmatrix}113&12\\120&113\end{bmatrix}$, $\begin{bmatrix}133&80\\140&1\end{bmatrix}$, $\begin{bmatrix}137&116\\44&65\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.192.5.cu.2 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $48$ |
| Cyclic 176-torsion field degree: | $480$ |
| Full 176-torsion field degree: | $844800$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| 16.192.2-16.d.1.1 | $16$ | $2$ | $2$ | $2$ | $0$ |
| 88.192.1-88.w.2.5 | $88$ | $2$ | $2$ | $1$ | $?$ |
| 176.192.1-88.w.2.8 | $176$ | $2$ | $2$ | $1$ | $?$ |
| 176.192.2-176.b.1.1 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.192.2-176.b.1.18 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.192.2-16.d.1.15 | $176$ | $2$ | $2$ | $2$ | $?$ |