Invariants
| Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $12^{6}$ | 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: | 12A4 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}17&86\\114&31\end{bmatrix}$, $\begin{bmatrix}61&32\\44&77\end{bmatrix}$, $\begin{bmatrix}81&8\\88&63\end{bmatrix}$, $\begin{bmatrix}83&114\\48&47\end{bmatrix}$, $\begin{bmatrix}89&110\\108&109\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.4.d.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| 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.a.1.12 | $24$ | $2$ | $2$ | $2$ | $1$ |
| 120.72.2-24.a.1.1 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.48.0-40.d.1.3 | $120$ | $3$ | $3$ | $0$ | $?$ |
| 60.72.2-60.b.1.6 | $60$ | $2$ | $2$ | $2$ | $0$ |
| 120.72.2-60.b.1.13 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.b.1.5 | $120$ | $2$ | $2$ | $2$ | $?$ |
| 120.72.2-120.b.1.30 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.fj.1.3 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fl.1.15 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fv.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.fx.1.8 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.kh.1.15 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.kj.1.10 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.kt.1.8 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.kv.1.3 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.pf.1.9 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.ph.1.10 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.pr.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.pt.1.4 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.rv.1.4 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.rx.1.12 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.sh.1.7 | $120$ | $2$ | $2$ | $7$ |
| 120.288.7-120.sj.1.3 | $120$ | $2$ | $2$ | $7$ |