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: | $6$ (none of which are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24J4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&58\\58&97\end{bmatrix}$, $\begin{bmatrix}16&15\\91&8\end{bmatrix}$, $\begin{bmatrix}25&8\\26&51\end{bmatrix}$, $\begin{bmatrix}37&94\\108&119\end{bmatrix}$, $\begin{bmatrix}100&81\\117&100\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.pp.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.co.1.15 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.2-24.co.1.27 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.22 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.cv.1.56 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dt.1.4 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.dt.1.14 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.bjd.1.32 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.bpa.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cgs.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.cgu.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dhi.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dhk.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.dio.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.diq.1.1 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.efg.1.11 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.efh.1.6 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.efv.1.15 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.efy.1.2 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ejg.1.20 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ejh.1.13 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.emn.1.22 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.emq.1.17 | $120$ | $2$ | $2$ | $7$ |