Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
| 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: | 8G0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}29&112\\27&79\end{bmatrix}$, $\begin{bmatrix}49&72\\9&35\end{bmatrix}$, $\begin{bmatrix}53&4\\96&97\end{bmatrix}$, $\begin{bmatrix}55&116\\92&119\end{bmatrix}$, $\begin{bmatrix}61&4\\5&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.24.0.bh.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $737280$ |
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 |
|---|---|---|---|---|---|
| 8.24.0-4.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 60.24.0-4.d.1.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0-120.y.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.y.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.y.1.17 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.y.1.32 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.96.1-120.ky.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.kz.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.la.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.lb.1.8 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.lc.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.ld.1.8 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.le.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.lf.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.144.4-120.ga.1.13 | $120$ | $3$ | $3$ | $4$ |
| 120.192.3-120.jk.1.3 | $120$ | $4$ | $4$ | $3$ |
| 120.240.8-120.cg.1.9 | $120$ | $5$ | $5$ | $8$ |
| 120.288.7-120.ceu.1.10 | $120$ | $6$ | $6$ | $7$ |
| 120.480.15-120.ga.1.2 | $120$ | $10$ | $10$ | $15$ |