Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2\cdot4\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8I0 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}0&171\\85&126\end{bmatrix}$, $\begin{bmatrix}26&91\\27&58\end{bmatrix}$, $\begin{bmatrix}30&137\\45&66\end{bmatrix}$, $\begin{bmatrix}64&35\\33&170\end{bmatrix}$, $\begin{bmatrix}157&88\\124&25\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 88.24.0.bu.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| Cyclic 176-torsion field degree: | $960$ |
| Full 176-torsion field degree: | $6758400$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 176.24.0-8.n.1.2 | $176$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 176.96.0-88.z.1.4 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bc.2.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bd.1.7 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.be.1.5 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bg.2.7 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bj.1.5 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bl.1.8 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-88.bm.1.7 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bc.2.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bi.2.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bk.1.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bq.1.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bs.2.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bu.2.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.bw.1.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.0-176.by.1.1 | $176$ | $2$ | $2$ | $0$ |
| 176.96.1-176.bg.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bi.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bk.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bm.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bo.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bu.1.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.bw.2.1 | $176$ | $2$ | $2$ | $1$ |
| 176.96.1-176.cc.2.1 | $176$ | $2$ | $2$ | $1$ |