Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24J4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}72&97\\115&22\end{bmatrix}$, $\begin{bmatrix}89&30\\86&49\end{bmatrix}$, $\begin{bmatrix}103&108\\70&77\end{bmatrix}$, $\begin{bmatrix}114&95\\43&18\end{bmatrix}$, $\begin{bmatrix}119&66\\108&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.ud.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 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.72.2-12.x.1.8 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 60.72.2-12.x.1.1 | $60$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.2-120.cv.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.48 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.db.1.18 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.db.1.44 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.biy.1.16 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bqu.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cid.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cif.1.14 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dcs.1.3 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dcy.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dej.1.3 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dep.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.evi.1.23 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.evl.1.14 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eyr.1.21 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.eyw.1.12 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fbm.1.10 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fbp.1.2 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fdh.1.4 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fdm.1.2 | $120$ | $2$ | $2$ | $7$ |