Invariants
| Level: | $120$ | $\SL_2$-level: | $30$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-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 | $6^{4}\cdot30^{4}$ | Cusp orbits | $4^{2}$ | ||
| 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: | 30K9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&33\\27&32\end{bmatrix}$, $\begin{bmatrix}40&113\\61&7\end{bmatrix}$, $\begin{bmatrix}43&44\\85&7\end{bmatrix}$, $\begin{bmatrix}115&26\\19&67\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=19,31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 60.72.1.fh.2 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.72.3.fui.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.72.3.gna.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.72.5.zm.1 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.72.5.bdl.2 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.72.5.beg.2 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.72.5.ciz.2 | $120$ | $2$ | $2$ | $5$ | $?$ |