Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot5^{2}\cdot8\cdot10\cdot40$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40F3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&92\\110&103\end{bmatrix}$, $\begin{bmatrix}46&75\\67&94\end{bmatrix}$, $\begin{bmatrix}67&42\\98&71\end{bmatrix}$, $\begin{bmatrix}74&23\\47&10\end{bmatrix}$, $\begin{bmatrix}86&105\\115&116\end{bmatrix}$, $\begin{bmatrix}105&34\\68&111\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.byf.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $8$ |
| Cyclic 120-torsion field degree: | $256$ |
| Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| $X_0(5)$ | $5$ | $24$ | $12$ | $0$ | $0$ |
| 24.24.0-24.z.1.6 | $24$ | $6$ | $6$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.24.0-24.z.1.6 | $24$ | $6$ | $6$ | $0$ | $0$ |
| 40.72.1-20.c.1.11 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 120.72.1-20.c.1.21 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.