Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&28\\108&91\end{bmatrix}$, $\begin{bmatrix}61&70\\88&71\end{bmatrix}$, $\begin{bmatrix}69&26\\40&3\end{bmatrix}$, $\begin{bmatrix}81&100\\56&81\end{bmatrix}$, $\begin{bmatrix}85&112\\112&41\end{bmatrix}$, $\begin{bmatrix}97&56\\48&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.9.ih.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no $\Q_p$ points for $p=127$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.5-24.g.1.7 | $24$ | $2$ | $2$ | $5$ | $1$ |
| 120.96.1-120.cd.2.8 | $120$ | $3$ | $3$ | $1$ | $?$ |
| 120.144.4-120.bo.1.19 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bo.1.123 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bp.2.48 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bp.2.101 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.5-24.g.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ |