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: | $\begin{bmatrix}1&0\\90&43\end{bmatrix}$, $\begin{bmatrix}7&84\\62&95\end{bmatrix}$, $\begin{bmatrix}55&24\\114&71\end{bmatrix}$, $\begin{bmatrix}55&84\\84&11\end{bmatrix}$, $\begin{bmatrix}91&60\\52&71\end{bmatrix}$, $\begin{bmatrix}109&96\\44&103\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.mm.2 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.3.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sl.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sl.2.25 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sy.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.1-120.sy.2.25 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-120.er.2.12 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.er.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.gc.1.66 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.gc.1.78 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sk.3.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sk.3.27 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sx.3.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.sx.3.27 | $120$ | $2$ | $2$ | $3$ | $?$ |