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: | $8$ (of which $2$ are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24I9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&56\\44&65\end{bmatrix}$, $\begin{bmatrix}25&68\\112&73\end{bmatrix}$, $\begin{bmatrix}29&16\\8&113\end{bmatrix}$, $\begin{bmatrix}47&86\\52&113\end{bmatrix}$, $\begin{bmatrix}59&32\\100&77\end{bmatrix}$, $\begin{bmatrix}69&22\\64&93\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.9.blr.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 60.144.4-60.p.1.11 | $60$ | $2$ | $2$ | $4$ | $1$ |
| 120.144.4-60.p.1.45 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-24.ch.1.37 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.5-120.p.1.27 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.144.5-120.p.1.56 | $120$ | $2$ | $2$ | $5$ | $?$ |