Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $9 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $8^{8}\cdot16^{8}$ | Cusp orbits | $1^{4}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16E9 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}81&170\\56&91\end{bmatrix}$, $\begin{bmatrix}97&66\\80&63\end{bmatrix}$, $\begin{bmatrix}113&132\\88&109\end{bmatrix}$, $\begin{bmatrix}137&70\\104&175\end{bmatrix}$, $\begin{bmatrix}145&150\\168&151\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.192.9.ga.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| 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 |
|---|---|---|---|---|---|
| 8.192.1-8.g.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 176.192.1-8.g.2.12 | $176$ | $2$ | $2$ | $1$ | $?$ |
| 176.192.5-176.ba.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.ba.2.4 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bb.2.4 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bb.2.23 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bj.1.1 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bj.1.16 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bq.2.2 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.bq.2.3 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.ci.1.2 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.ci.1.7 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.cj.1.1 | $176$ | $2$ | $2$ | $5$ | $?$ |
| 176.192.5-176.cj.1.16 | $176$ | $2$ | $2$ | $5$ | $?$ |