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: | $\begin{bmatrix}42&97\\55&96\end{bmatrix}$, $\begin{bmatrix}45&16\\52&45\end{bmatrix}$, $\begin{bmatrix}47&52\\92&95\end{bmatrix}$, $\begin{bmatrix}82&25\\17&94\end{bmatrix}$, $\begin{bmatrix}100&69\\63&46\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.cbz.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 no real points and no $\Q_p$ points for $p=19$, and therefore no 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.cm.1.31 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.1-120.bh.1.20 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.72.1-120.bh.1.26 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.72.2-24.cm.1.2 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.49 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.7-120.bgo.1.36 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqf.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cfm.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cfp.1.8 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dgr.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dgw.1.5 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dio.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dir.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fbk.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fbp.1.2 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fcp.1.15 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fcw.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fga.1.19 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fgf.1.6 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fit.1.21 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fja.1.11 | $120$ | $2$ | $2$ | $7$ |