Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16C5 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}39&120\\102&165\end{bmatrix}$, $\begin{bmatrix}83&106\\2&95\end{bmatrix}$, $\begin{bmatrix}101&80\\150&171\end{bmatrix}$, $\begin{bmatrix}139&108\\66&113\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.96.5.bp.2 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $48$ |
| Cyclic 176-torsion field degree: | $1920$ |
| Full 176-torsion field degree: | $1689600$ |
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 |
|---|---|---|---|---|---|
| 8.96.1-8.i.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 176.96.1-8.i.2.2 | $176$ | $2$ | $2$ | $1$ | $?$ |
| 176.96.3-176.d.2.3 | $176$ | $2$ | $2$ | $3$ | $?$ |
| 176.96.3-176.d.2.4 | $176$ | $2$ | $2$ | $3$ | $?$ |
| 176.96.3-176.f.1.8 | $176$ | $2$ | $2$ | $3$ | $?$ |
| 176.96.3-176.f.1.22 | $176$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.384.9-176.da.2.12 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.dk.2.1 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.ds.1.7 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.ea.2.2 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.fl.2.6 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.ft.1.5 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.ga.4.4 | $176$ | $2$ | $2$ | $9$ |
| 176.384.9-176.go.1.14 | $176$ | $2$ | $2$ | $9$ |