Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16J3 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}3&42\\64&97\end{bmatrix}$, $\begin{bmatrix}81&90\\112&93\end{bmatrix}$, $\begin{bmatrix}87&70\\120&145\end{bmatrix}$, $\begin{bmatrix}109&152\\64&173\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.96.3.cm.2 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| Cyclic 176-torsion field degree: | $960$ |
| 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 |
|---|---|---|---|---|---|
| 16.96.1-16.b.2.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 88.96.0-88.z.2.5 | $88$ | $2$ | $2$ | $0$ | $?$ |
| 176.96.0-88.z.2.6 | $176$ | $2$ | $2$ | $0$ | $?$ |
| 176.96.1-16.b.2.8 | $176$ | $2$ | $2$ | $1$ | $?$ |
| 176.96.2-176.d.1.5 | $176$ | $2$ | $2$ | $2$ | $?$ |
| 176.96.2-176.d.1.20 | $176$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.384.5-176.y.2.4 | $176$ | $2$ | $2$ | $5$ |
| 176.384.5-176.cm.1.2 | $176$ | $2$ | $2$ | $5$ |
| 176.384.5-176.ei.1.4 | $176$ | $2$ | $2$ | $5$ |
| 176.384.5-176.em.1.2 | $176$ | $2$ | $2$ | $5$ |