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: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| 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: | 8N0 |
Level structure
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 |
|---|---|---|---|---|---|
| 8.24.0.e.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 60.24.0.c.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0.t.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.be.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.da.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.dy.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.eg.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.iz.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.jh.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.jo.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.jw.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.mu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.nc.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.nl.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.nt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.pg.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.po.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.pt.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1.px.1 | $120$ | $2$ | $2$ | $1$ |
| 120.144.8.dn.2 | $120$ | $3$ | $3$ | $8$ |
| 120.192.7.dj.1 | $120$ | $4$ | $4$ | $7$ |
| 120.240.16.bt.2 | $120$ | $5$ | $5$ | $16$ |
| 120.288.15.wr.2 | $120$ | $6$ | $6$ | $15$ |