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: | $\begin{bmatrix}15&118\\26&73\end{bmatrix}$, $\begin{bmatrix}67&102\\6&43\end{bmatrix}$, $\begin{bmatrix}85&68\\106&21\end{bmatrix}$, $\begin{bmatrix}119&88\\102&13\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.pq.2 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 |
|---|---|---|---|---|---|
| 24.192.3-24.bz.2.5 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 60.192.1-60.f.4.3 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-60.f.4.11 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lj.4.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lj.4.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lv.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.lv.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-24.bz.2.16 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.eg.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.eg.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.gh.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.gh.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.go.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.go.1.28 | $120$ | $2$ | $2$ | $3$ | $?$ |