Invariants
| Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$ | Cusp orbits | $2^{4}$ | ||
| 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: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20J3 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}43&0\\83&61\end{bmatrix}$, $\begin{bmatrix}61&10\\72&89\end{bmatrix}$, $\begin{bmatrix}69&40\\89&27\end{bmatrix}$, $\begin{bmatrix}71&0\\75&49\end{bmatrix}$, $\begin{bmatrix}71&20\\29&79\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| Full 120-torsion field degree: | $491520$ |
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 |
|---|---|---|---|---|---|
| 40.36.1.k.1 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 60.36.1.bg.1 | $60$ | $2$ | $2$ | $1$ | $1$ |
| 120.12.0.ec.1 | $120$ | $6$ | $6$ | $0$ | $?$ |
| 120.36.1.dx.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.144.5.ens.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.ens.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.ent.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.ent.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.enz.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.enz.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eoa.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eoa.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.epw.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.epw.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.epx.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.epx.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eqd.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eqd.2 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eqe.1 | $120$ | $2$ | $2$ | $5$ |
| 120.144.5.eqe.2 | $120$ | $2$ | $2$ | $5$ |
| 120.216.15.bmq.1 | $120$ | $3$ | $3$ | $15$ |
| 120.288.17.cmtw.1 | $120$ | $4$ | $4$ | $17$ |
| 120.360.19.ewy.1 | $120$ | $5$ | $5$ | $19$ |