Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | 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: | $8$ (none of which are rational) | Cusp widths | $3^{4}\cdot6^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| 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: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24L3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}28&109\\103&50\end{bmatrix}$, $\begin{bmatrix}62&113\\101&22\end{bmatrix}$, $\begin{bmatrix}88&9\\57&100\end{bmatrix}$, $\begin{bmatrix}91&118\\110&91\end{bmatrix}$, $\begin{bmatrix}108&41\\83&90\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.cdo.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $245760$ |
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 |
|---|---|---|---|---|---|
| 24.72.2-24.cw.1.15 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 60.72.1-60.j.1.2 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.72.1-60.j.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.72.2-24.cw.1.14 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.de.1.14 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.de.1.33 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.