Invariants
| Level: | $120$ | $\SL_2$-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 |
|---|---|---|---|---|---|
| 24.24.0.h.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 40.24.0.l.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0.u.2 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.96.1.e.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.l.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.bx.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.cf.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.dk.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.dl.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.do.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.dp.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.ic.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.id.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.im.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.in.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.ji.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.jj.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.js.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.jt.2 | $120$ | $2$ | $2$ | $1$ |
| 120.144.8.nf.2 | $120$ | $3$ | $3$ | $8$ |
| 120.192.7.hp.1 | $120$ | $4$ | $4$ | $7$ |
| 120.240.16.cv.2 | $120$ | $5$ | $5$ | $16$ |
| 120.288.15.caz.1 | $120$ | $6$ | $6$ | $15$ |