Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $9 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $20^{2}\cdot40^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B9 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&10\\98&21\end{bmatrix}$, $\begin{bmatrix}16&19\\87&112\end{bmatrix}$, $\begin{bmatrix}29&18\\70&23\end{bmatrix}$, $\begin{bmatrix}43&80\\48&101\end{bmatrix}$, $\begin{bmatrix}89&10\\34&13\end{bmatrix}$ |
| 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: | $294912$ |
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 |
|---|---|---|---|---|---|
| 40.60.5.d.1 | $40$ | $2$ | $2$ | $5$ | $1$ |
| 60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
| 120.24.1.bt.1 | $120$ | $5$ | $5$ | $1$ | $?$ |
| 120.60.4.gu.1 | $120$ | $2$ | $2$ | $4$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.240.17.r.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.mv.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.tl.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.up.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.yt.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.yv.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bbc.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bbi.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bdd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bdf.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bew.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bfc.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bfp.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bfr.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bju.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bka.1 | $120$ | $2$ | $2$ | $17$ |