Invariants
| Level: | $120$ | $\SL_2$-level: | $60$ | 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: | $12$ (of which $4$ are rational) | Cusp widths | $2^{3}\cdot6^{3}\cdot10^{3}\cdot30^{3}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30S7 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&106\\60&61\end{bmatrix}$, $\begin{bmatrix}19&27\\60&49\end{bmatrix}$, $\begin{bmatrix}41&28\\50&51\end{bmatrix}$, $\begin{bmatrix}53&100\\20&69\end{bmatrix}$, $\begin{bmatrix}79&119\\0&113\end{bmatrix}$, $\begin{bmatrix}113&45\\110&79\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.7.hmw.2 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $4$ |
| Cyclic 120-torsion field degree: | $128$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 60.144.3-30.a.1.9 | $60$ | $2$ | $2$ | $3$ | $0$ |
| 120.144.3-30.a.1.48 | $120$ | $2$ | $2$ | $3$ | $?$ |