Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{6}\cdot4\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16O5 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}17&68\\96&135\end{bmatrix}$, $\begin{bmatrix}23&136\\8&47\end{bmatrix}$, $\begin{bmatrix}71&116\\108&113\end{bmatrix}$, $\begin{bmatrix}107&92\\132&23\end{bmatrix}$, $\begin{bmatrix}155&92\\12&95\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 176.384.5-176.cx.1.1, 176.384.5-176.cx.1.2, 176.384.5-176.cx.1.3, 176.384.5-176.cx.1.4, 176.384.5-176.cx.1.5, 176.384.5-176.cx.1.6, 176.384.5-176.cx.1.7, 176.384.5-176.cx.1.8, 176.384.5-176.cx.1.9, 176.384.5-176.cx.1.10, 176.384.5-176.cx.1.11, 176.384.5-176.cx.1.12, 176.384.5-176.cx.1.13, 176.384.5-176.cx.1.14, 176.384.5-176.cx.1.15, 176.384.5-176.cx.1.16 |
| Cyclic 176-isogeny field degree: | $48$ |
| Cyclic 176-torsion field degree: | $1920$ |
| Full 176-torsion field degree: | $1689600$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.96.1.f.2 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 176.96.2.c.1 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.96.2.d.1 | $176$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.384.13.dl.2 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.dm.1 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.dn.1 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.dr.2 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.eb.1 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.ed.2 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.eq.2 | $176$ | $2$ | $2$ | $13$ |
| 176.384.13.er.2 | $176$ | $2$ | $2$ | $13$ |