Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $13 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $5^{8}\cdot10^{4}\cdot40^{4}$ | Cusp orbits | $4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 24$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 13$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40G13 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&50\\56&69\end{bmatrix}$, $\begin{bmatrix}25&54\\14&5\end{bmatrix}$, $\begin{bmatrix}37&42\\4&103\end{bmatrix}$, $\begin{bmatrix}97&80\\62&3\end{bmatrix}$, $\begin{bmatrix}98&89\\11&12\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.13.cbw.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11,13$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.7-40.cp.1.6 | $40$ | $2$ | $2$ | $7$ | $1$ |
| 60.240.5-60.m.1.5 | $60$ | $2$ | $2$ | $5$ | $0$ |
| 120.240.5-60.m.1.22 | $120$ | $2$ | $2$ | $5$ | $?$ |
| 120.240.7-40.cp.1.14 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.41 | $120$ | $2$ | $2$ | $7$ | $?$ |