Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M1 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}31&16\\75&85\end{bmatrix}$, $\begin{bmatrix}45&0\\113&109\end{bmatrix}$, $\begin{bmatrix}175&168\\104&129\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.96.1.ej.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| Cyclic 176-torsion field degree: | $480$ |
| Full 176-torsion field degree: | $1689600$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 16.96.0-16.z.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 176.96.0-16.z.1.3 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 88.96.0-88.bl.2.5 | $88$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.0-88.bl.2.3 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.0-176.y.1.4 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.0-176.y.1.9 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.0-176.bw.2.6 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.0-176.bw.2.13 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 176.96.1-176.bo.2.4 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bo.2.11 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.br.1.6 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.br.1.13 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.ck.1.8 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.ck.1.15 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |