Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $8^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3$ | ||||||
| $\overline{\Q}$-gonality: | $3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16A3 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}45&38\\70&109\end{bmatrix}$, $\begin{bmatrix}129&26\\106&101\end{bmatrix}$, $\begin{bmatrix}144&57\\161&104\end{bmatrix}$, $\begin{bmatrix}153&136\\168&133\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.48.3.bd.2 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $48$ |
| Cyclic 176-torsion field degree: | $3840$ |
| Full 176-torsion field degree: | $3379200$ |
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 |
|---|---|---|---|---|---|
| 8.48.1-8.n.1.4 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 176.48.1-8.n.1.1 | $176$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.192.5-176.ea.2.1 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.eb.1.9 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.fv.2.3 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.fx.1.4 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.gh.1.4 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.gj.1.2 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.gt.1.5 | $176$ | $2$ | $2$ | $5$ |
| 176.192.5-176.gu.1.1 | $176$ | $2$ | $2$ | $5$ |