Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{4}\cdot40^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A17 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&75\\112&13\end{bmatrix}$, $\begin{bmatrix}43&85\\20&93\end{bmatrix}$, $\begin{bmatrix}55&44\\56&99\end{bmatrix}$, $\begin{bmatrix}109&65\\68&47\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.17.ty.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.8-20.g.1.6 | $40$ | $2$ | $2$ | $8$ | $2$ |
| 60.240.8-20.g.1.1 | $60$ | $2$ | $2$ | $8$ | $2$ |
| 120.96.1-120.ms.1.3 | $120$ | $5$ | $5$ | $1$ | $?$ |
| 120.240.8-120.ct.1.9 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.ct.1.11 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.9-120.z.1.9 | $120$ | $2$ | $2$ | $9$ | $?$ |
| 120.240.9-120.z.1.11 | $120$ | $2$ | $2$ | $9$ | $?$ |