Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $20^{2}\cdot40^{2}$ | Cusp orbits | $2^{2}$ | ||
| Elliptic points: | $4$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40B8 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&44\\96&53\end{bmatrix}$, $\begin{bmatrix}13&52\\28&35\end{bmatrix}$, $\begin{bmatrix}57&46\\118&111\end{bmatrix}$, $\begin{bmatrix}86&35\\103&74\end{bmatrix}$, $\begin{bmatrix}89&90\\58&17\end{bmatrix}$ |
| 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 no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.60.4.cr.1 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
| 120.24.0.nx.1 | $120$ | $5$ | $5$ | $0$ | $?$ |
| 120.60.4.hr.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.eg.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.mn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.uw.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.vf.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.zb.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.zn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.baw.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.bbi.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jep.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jev.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jiy.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jja.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jlj.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jlp.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jng.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.jni.1 | $120$ | $2$ | $2$ | $17$ |
| 120.360.22.btv.1 | $120$ | $3$ | $3$ | $22$ |