Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $4^{4}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8A5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&50\\16&3\end{bmatrix}$, $\begin{bmatrix}21&10\\104&63\end{bmatrix}$, $\begin{bmatrix}99&50\\92&41\end{bmatrix}$, $\begin{bmatrix}103&78\\72&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.ci.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $92160$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=29$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.q.1.15 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 40.192.1-40.e.2.4 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-40.e.2.10 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.n.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.n.2.22 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.bm.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.bm.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-24.q.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.y.1.7 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.y.1.24 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bq.2.11 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bq.2.30 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bz.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bz.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ |