Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-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 | $2^{4}\cdot8^{2}$ | 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: | 8G0 |
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 |
|---|---|---|---|---|---|
| $X_0(8)$ | $8$ | $2$ | $2$ | $0$ | $0$ |
| 60.12.0.h.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.12.0.z.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.48.0.el.1 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.el.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.em.1 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.em.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.en.1 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.en.2 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.eo.1 | $120$ | $2$ | $2$ | $0$ |
| 120.48.0.eo.2 | $120$ | $2$ | $2$ | $0$ |
| 120.72.4.mf.1 | $120$ | $3$ | $3$ | $4$ |
| 120.96.3.pn.1 | $120$ | $4$ | $4$ | $3$ |
| 120.120.8.ff.1 | $120$ | $5$ | $5$ | $8$ |
| 120.144.7.dvs.1 | $120$ | $6$ | $6$ | $7$ |
| 120.240.15.lx.1 | $120$ | $10$ | $10$ | $15$ |
| 240.48.0.ca.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.ca.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cb.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cb.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cc.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cc.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cd.1 | $240$ | $2$ | $2$ | $0$ |
| 240.48.0.cd.2 | $240$ | $2$ | $2$ | $0$ |
| 240.48.1.u.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.w.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.eh.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ei.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.hj.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.hk.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.hy.1 | $240$ | $2$ | $2$ | $1$ |
| 240.48.1.ia.1 | $240$ | $2$ | $2$ | $1$ |