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 | $2^{4}\cdot4^{2}\cdot8$ | ||
| 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: | $\begin{bmatrix}5&76\\92&21\end{bmatrix}$, $\begin{bmatrix}53&34\\116&27\end{bmatrix}$, $\begin{bmatrix}77&72\\52&13\end{bmatrix}$, $\begin{bmatrix}105&88\\112&109\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.hu.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $384$ |
| Full 120-torsion field degree: | $92160$ |
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 |
|---|---|---|---|---|---|
| 24.192.1-24.x.1.1 | $24$ | $2$ | $2$ | $1$ | $0$ |
| 40.192.1-40.x.2.5 | $40$ | $2$ | $2$ | $1$ | $1$ |
| 120.192.1-24.x.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-40.x.2.12 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.bp.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.bp.1.17 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-120.bx.3.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bx.3.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bz.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.bz.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.cd.2.9 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.cd.2.17 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.cw.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.cw.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |