Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20J3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&10\\76&43\end{bmatrix}$, $\begin{bmatrix}23&60\\40&113\end{bmatrix}$, $\begin{bmatrix}27&10\\10&103\end{bmatrix}$, $\begin{bmatrix}51&10\\16&27\end{bmatrix}$, $\begin{bmatrix}57&50\\28&27\end{bmatrix}$, $\begin{bmatrix}63&40\\64&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.a.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| Full 120-torsion field degree: | $245760$ |
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 |
|---|---|---|---|---|---|
| 40.72.1-10.a.1.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 60.72.1-10.a.1.8 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.24.0-24.a.1.8 | $120$ | $6$ | $6$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.