Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $4$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8H0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}18&53\\17&94\end{bmatrix}$, $\begin{bmatrix}26&7\\93&70\end{bmatrix}$, $\begin{bmatrix}42&77\\85&34\end{bmatrix}$, $\begin{bmatrix}82&15\\113&98\end{bmatrix}$, $\begin{bmatrix}115&86\\22&111\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $1474560$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 8.12.0.y.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.12.0.eq.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.48.1.j.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.fu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.mf.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.mv.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwb.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwd.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bxu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bya.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ckr.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ckt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cmk.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cmq.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cnd.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cnf.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cry.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cse.1 | $120$ | $2$ | $2$ | $1$ |
| 120.72.2.bbr.1 | $120$ | $3$ | $3$ | $2$ |
| 120.96.5.bdp.1 | $120$ | $4$ | $4$ | $5$ |
| 120.120.8.tz.1 | $120$ | $5$ | $5$ | $8$ |
| 120.144.7.lvj.1 | $120$ | $6$ | $6$ | $7$ |
| 120.240.15.dll.1 | $120$ | $10$ | $10$ | $15$ |