Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $60$ | ||||
| Genus: | $4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $10^{2}\cdot20^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&8\\46&1\end{bmatrix}$, $\begin{bmatrix}17&77\\24&97\end{bmatrix}$, $\begin{bmatrix}63&28\\98&37\end{bmatrix}$, $\begin{bmatrix}113&92\\4&105\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.60.4.y.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $294912$ |
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 |
|---|---|---|---|---|---|
| 40.60.2-20.b.1.6 | $40$ | $2$ | $2$ | $2$ | $0$ |
| 120.24.0-24.m.1.2 | $120$ | $5$ | $5$ | $0$ | $?$ |
| 120.60.2-20.b.1.2 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.360.10-120.bw.1.11 | $120$ | $3$ | $3$ | $10$ |
| 120.360.14-120.ds.1.6 | $120$ | $3$ | $3$ | $14$ |
| 120.480.13-120.bcb.1.3 | $120$ | $4$ | $4$ | $13$ |
| 120.480.17-120.bpq.1.19 | $120$ | $4$ | $4$ | $17$ |