Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $160$ | $\PSL_2$-index: | $160$ | ||||
| Genus: | $9 = 1 + \frac{ 160 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{8}$ | Cusp orbits | $8$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&67\\108&107\end{bmatrix}$, $\begin{bmatrix}85&7\\12&35\end{bmatrix}$, $\begin{bmatrix}92&1\\3&53\end{bmatrix}$, $\begin{bmatrix}114&11\\109&10\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $288$ |
| Cyclic 120-torsion field degree: | $9216$ |
| Full 120-torsion field degree: | $221184$ |
Rational points
This modular curve has no real points, and therefore no 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 |
|---|---|---|---|---|---|
| 8.8.0.b.1 | $8$ | $20$ | $20$ | $0$ | $0$ |
| 15.20.0.b.1 | $15$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.80.5.b.1 | $40$ | $2$ | $2$ | $5$ | $3$ |
| 60.80.5.o.1 | $60$ | $2$ | $2$ | $5$ | $4$ |
| 120.40.1.t.1 | $120$ | $4$ | $4$ | $1$ | $?$ |
| 120.80.3.i.1 | $120$ | $2$ | $2$ | $3$ | $?$ |