Invariants
| Level: | $120$ | $\SL_2$-level: | $4$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2\cdot4$ | ||
| Elliptic points: | $0$ 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: | 4G0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}12&31\\53&52\end{bmatrix}$, $\begin{bmatrix}44&63\\63&64\end{bmatrix}$, $\begin{bmatrix}53&28\\112&55\end{bmatrix}$, $\begin{bmatrix}102&1\\77&110\end{bmatrix}$, $\begin{bmatrix}115&98\\42&95\end{bmatrix}$ |
| 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.f.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.12.0.ep.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.fu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.fw.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.fy.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ge.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.go.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.gu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.gw.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.hk.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.hm.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ia.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ic.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ii.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.ik.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.iq.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.is.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.iu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.72.4.fj.1 | $120$ | $3$ | $3$ | $4$ |
| 120.96.3.ib.1 | $120$ | $4$ | $4$ | $3$ |
| 120.120.8.bw.1 | $120$ | $5$ | $5$ | $8$ |
| 120.144.7.brm.1 | $120$ | $6$ | $6$ | $7$ |
| 120.240.15.fk.1 | $120$ | $10$ | $10$ | $15$ |