Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 30$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B16 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}15&53\\104&35\end{bmatrix}$, $\begin{bmatrix}43&90\\40&13\end{bmatrix}$, $\begin{bmatrix}45&56\\104&9\end{bmatrix}$, $\begin{bmatrix}97&45\\32&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.16.gk.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.8-40.da.1.5 | $40$ | $2$ | $2$ | $8$ | $2$ |
| 120.96.0-120.ep.2.12 | $120$ | $5$ | $5$ | $0$ | $?$ |
| 120.240.8-40.da.1.5 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.fh.1.12 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.fh.1.18 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.gh.1.14 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.240.8-120.gh.1.29 | $120$ | $2$ | $2$ | $8$ | $?$ |