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: | $\begin{bmatrix}9&44\\44&67\end{bmatrix}$, $\begin{bmatrix}15&8\\26&65\end{bmatrix}$, $\begin{bmatrix}75&52\\11&43\end{bmatrix}$, $\begin{bmatrix}77&32\\12&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.24.0.cq.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 |
|---|---|---|---|---|---|
| 40.24.0-20.h.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0-20.h.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 24.24.0-24.y.1.16 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 120.24.0-24.y.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.y.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.24.0-120.y.1.10 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.144.4-120.ka.1.23 | $120$ | $3$ | $3$ | $4$ |
| 120.192.3-120.oo.1.10 | $120$ | $4$ | $4$ | $3$ |
| 120.240.8-120.eo.1.6 | $120$ | $5$ | $5$ | $8$ |
| 120.288.7-120.dur.1.13 | $120$ | $6$ | $6$ | $7$ |
| 120.480.15-120.kq.1.22 | $120$ | $10$ | $10$ | $15$ |