Invariants
| Level: | $168$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-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
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 |
|---|---|---|---|---|---|
| 8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 168.24.0.u.2 | $168$ | $2$ | $2$ | $0$ | $?$ |
| 168.24.0.y.1 | $168$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 168.96.1.b.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.c.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ca.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.cd.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ei.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.ej.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.eq.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.er.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.fq.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.fr.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.fy.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.fz.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.hm.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.hn.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.hu.1 | $168$ | $2$ | $2$ | $1$ |
| 168.96.1.hv.1 | $168$ | $2$ | $2$ | $1$ |
| 168.144.8.mg.2 | $168$ | $3$ | $3$ | $8$ |
| 168.192.7.gs.2 | $168$ | $4$ | $4$ | $7$ |
| 168.384.23.hm.2 | $168$ | $8$ | $8$ | $23$ |