Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot20^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20D5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&54\\38&5\end{bmatrix}$, $\begin{bmatrix}71&3\\30&109\end{bmatrix}$, $\begin{bmatrix}87&64\\43&73\end{bmatrix}$, $\begin{bmatrix}113&43\\24&107\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.96.5.ip.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $184320$ |
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 |
|---|---|---|---|---|---|
| 20.96.3-20.i.2.6 | $20$ | $2$ | $2$ | $3$ | $0$ |
| 120.48.1-120.et.2.7 | $120$ | $4$ | $4$ | $1$ | $?$ |
| 120.96.3-20.i.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ |