Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | 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 | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $2^{8}\cdot4^{2}$ | ||
| 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: | 24Z5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&12\\2&97\end{bmatrix}$, $\begin{bmatrix}19&96\\76&53\end{bmatrix}$, $\begin{bmatrix}43&36\\84&89\end{bmatrix}$, $\begin{bmatrix}49&0\\40&61\end{bmatrix}$, $\begin{bmatrix}79&12\\42&107\end{bmatrix}$, $\begin{bmatrix}85&96\\6&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.ly.3 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| 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 |
|---|---|---|---|---|---|
| 12.192.1-12.b.3.2 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-12.b.3.10 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.ss.4.12 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.ss.4.21 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sv.4.12 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sv.4.21 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-120.eq.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.eq.1.34 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fz.1.48 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.fz.1.55 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sn.4.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sn.4.27 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sq.4.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sq.4.27 | $120$ | $2$ | $2$ | $3$ | $?$ |