Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{8}\cdot40^{4}$ | Cusp orbits | $4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40E15 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&111\\76&47\end{bmatrix}$, $\begin{bmatrix}21&16\\76&39\end{bmatrix}$, $\begin{bmatrix}53&11\\0&97\end{bmatrix}$, $\begin{bmatrix}55&97\\68&75\end{bmatrix}$, $\begin{bmatrix}119&6\\16&101\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.240.15.ui.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 real points and $\Q_p$ points for $p$ not dividing the level, but no known 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.ct.1.19 | $40$ | $2$ | $2$ | $7$ | $4$ |
| 120.240.7-40.ct.1.20 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.2 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.ef.1.10 | $120$ | $2$ | $2$ | $7$ | $?$ |
| 120.240.7-120.ef.1.19 | $120$ | $2$ | $2$ | $7$ | $?$ |