Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12E5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&36\\40&23\end{bmatrix}$, $\begin{bmatrix}35&88\\14&69\end{bmatrix}$, $\begin{bmatrix}39&10\\14&103\end{bmatrix}$, $\begin{bmatrix}53&54\\90&47\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.jq.3 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $92160$ |
Rational points
This modular curve has no $\Q_p$ points for $p=23$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.1-24.cl.1.9 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 60.192.1-60.g.3.6 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-60.g.3.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-24.cl.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lx.4.6 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lx.4.30 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-120.ea.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ea.1.9 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fc.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fc.2.15 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fr.2.4 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fr.2.27 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ft.2.14 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ft.2.20 | $120$ | $2$ | $2$ | $3$ | $?$ |