Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}\cdot12^{8}\cdot24^{2}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AG7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}43&88\\108&47\end{bmatrix}$, $\begin{bmatrix}59&32\\96&55\end{bmatrix}$, $\begin{bmatrix}63&74\\16&7\end{bmatrix}$, $\begin{bmatrix}69&62\\92&105\end{bmatrix}$, $\begin{bmatrix}115&66\\12&109\end{bmatrix}$, $\begin{bmatrix}117&104\\100&73\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.7.de.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 no $\Q_p$ points for $p=47$, 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.bn.1.31 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 60.192.3-60.f.1.5 | $60$ | $2$ | $2$ | $3$ | $1$ |
| 120.96.0-120.z.1.6 | $120$ | $4$ | $4$ | $0$ | $?$ |
| 120.192.3-60.f.1.37 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-24.bn.1.4 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.eu.2.62 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.eu.2.67 | $120$ | $2$ | $2$ | $3$ | $?$ |