Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40M7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&60\\88&77\end{bmatrix}$, $\begin{bmatrix}23&20\\25&117\end{bmatrix}$, $\begin{bmatrix}57&80\\113&119\end{bmatrix}$, $\begin{bmatrix}59&100\\16&63\end{bmatrix}$, $\begin{bmatrix}109&80\\90&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.7.dxb.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $8$ |
| Cyclic 120-torsion field degree: | $128$ |
| Full 120-torsion field degree: | $122880$ |
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 |
|---|---|---|---|---|---|
| 40.144.3-40.ce.1.4 | $40$ | $2$ | $2$ | $3$ | $1$ |
| 60.144.3-60.ff.1.1 | $60$ | $2$ | $2$ | $3$ | $1$ |
| 120.48.0-120.ea.1.7 | $120$ | $6$ | $6$ | $0$ | $?$ |
| 120.144.3-40.ce.1.5 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-60.ff.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.byo.1.36 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.144.3-120.byo.1.41 | $120$ | $2$ | $2$ | $3$ | $?$ |