Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}97&160\\41&139\end{bmatrix}$, $\begin{bmatrix}103&104\\38&23\end{bmatrix}$, $\begin{bmatrix}147&72\\137&71\end{bmatrix}$, $\begin{bmatrix}155&136\\72&119\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.48.0.bm.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| Cyclic 176-torsion field degree: | $960$ |
| Full 176-torsion field degree: | $3379200$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 16.48.0-8.ba.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 176.48.0-8.ba.1.2 | $176$ | $2$ | $2$ | $0$ | $?$ |
| 176.48.0-88.bl.1.4 | $176$ | $2$ | $2$ | $0$ | $?$ |
| 176.48.0-88.bl.1.5 | $176$ | $2$ | $2$ | $0$ | $?$ |
| 176.48.0-88.bu.1.3 | $176$ | $2$ | $2$ | $0$ | $?$ |
| 176.48.0-88.bu.1.11 | $176$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.192.1-176.cy.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.da.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.dg.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.di.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.ee.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.eg.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.em.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.192.1-176.eo.1.1 | $176$ | $2$ | $2$ | $1$ |