Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-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: | $\begin{bmatrix}1&20\\108&17\end{bmatrix}$, $\begin{bmatrix}1&110\\64&43\end{bmatrix}$, $\begin{bmatrix}33&40\\1&57\end{bmatrix}$, $\begin{bmatrix}57&40\\68&97\end{bmatrix}$, $\begin{bmatrix}67&10\\25&83\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.72.3.bgm.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $16$ |
| Cyclic 120-torsion field degree: | $512$ |
| 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 |
|---|---|---|---|---|---|
| 40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ |
| 120.24.0-120.m.1.4 | $120$ | $6$ | $6$ | $0$ | $?$ |
| 120.72.1-20.b.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.288.5-120.bob.1.8 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bob.2.8 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boc.1.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boc.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boi.1.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boi.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boj.1.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.boj.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqf.1.7 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqf.2.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqg.1.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqg.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqm.1.7 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqm.2.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqn.1.6 | $120$ | $2$ | $2$ | $5$ |
| 120.288.5-120.bqn.2.4 | $120$ | $2$ | $2$ | $5$ |
| 120.432.15-120.gm.1.13 | $120$ | $3$ | $3$ | $15$ |