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 | $2^{2}\cdot4^{5}$ | ||
| 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: | 24Z5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&36\\118&49\end{bmatrix}$, $\begin{bmatrix}25&24\\42&79\end{bmatrix}$, $\begin{bmatrix}25&84\\53&113\end{bmatrix}$, $\begin{bmatrix}91&24\\15&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.bie.1 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 |
|---|---|---|---|---|---|
| 24.192.3-24.gz.3.8 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 60.192.1-60.m.1.4 | $60$ | $2$ | $2$ | $1$ | $1$ |
| 120.192.1-60.m.1.23 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sy.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sy.2.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.tg.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.tg.1.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-24.gz.3.9 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.pf.1.3 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.pf.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.rc.1.15 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.rc.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.tv.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.tv.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ |