Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | 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: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&38\\118&117\end{bmatrix}$, $\begin{bmatrix}69&56\\82&9\end{bmatrix}$, $\begin{bmatrix}75&44\\2&65\end{bmatrix}$, $\begin{bmatrix}75&94\\88&109\end{bmatrix}$, $\begin{bmatrix}91&84\\88&119\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.60.4.b.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 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $24$ | $12$ | $0$ | $0$ |
| 24.24.0-24.b.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.0-24.b.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
| 40.60.2-10.a.1.1 | $40$ | $2$ | $2$ | $2$ | $0$ |
| 60.60.2-10.a.1.1 | $60$ | $2$ | $2$ | $2$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.240.8-120.c.1.3 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.c.1.15 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.d.1.8 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.d.1.14 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.e.1.11 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.e.1.23 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.f.1.12 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.f.1.14 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.v.1.11 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.v.1.15 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.w.1.3 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.w.1.4 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.y.1.11 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.y.1.15 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.z.1.11 | $120$ | $2$ | $2$ | $8$ |
| 120.240.8-120.z.1.13 | $120$ | $2$ | $2$ | $8$ |
| 120.360.10-120.b.1.6 | $120$ | $3$ | $3$ | $10$ |
| 120.360.14-120.d.1.26 | $120$ | $3$ | $3$ | $14$ |
| 120.480.13-120.cx.1.3 | $120$ | $4$ | $4$ | $13$ |
| 120.480.17-120.fj.1.3 | $120$ | $4$ | $4$ | $17$ |