Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $360$ | $\PSL_2$-index: | $360$ | ||||
| Genus: | $22 = 1 + \frac{ 360 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $10^{12}\cdot40^{6}$ | Cusp orbits | $2^{3}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 42$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 22$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A22 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&115\\100&93\end{bmatrix}$, $\begin{bmatrix}17&42\\24&43\end{bmatrix}$, $\begin{bmatrix}17&42\\84&53\end{bmatrix}$, $\begin{bmatrix}21&52\\40&119\end{bmatrix}$, $\begin{bmatrix}49&83\\96&41\end{bmatrix}$, $\begin{bmatrix}103&96\\60&17\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| Full 120-torsion field degree: | $98304$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7,31$, 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{sp}}^+(5)$ | $5$ | $24$ | $24$ | $0$ | $0$ |
| 24.24.0.bk.1 | $24$ | $15$ | $15$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.180.10.ci.1 | $40$ | $2$ | $2$ | $10$ | $1$ |
| 60.180.10.t.1 | $60$ | $2$ | $2$ | $10$ | $2$ |
| 120.120.8.de.1 | $120$ | $3$ | $3$ | $8$ | $?$ |
| 120.180.10.cu.1 | $120$ | $2$ | $2$ | $10$ | $?$ |