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: | $\begin{bmatrix}12&55\\19&76\end{bmatrix}$, $\begin{bmatrix}13&58\\58&47\end{bmatrix}$, $\begin{bmatrix}73&16\\64&117\end{bmatrix}$, $\begin{bmatrix}86&73\\29&26\end{bmatrix}$, $\begin{bmatrix}92&113\\117&80\end{bmatrix}$ |
| 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.cl.1 | $40$ | $2$ | $2$ | $4$ | $1$ |
| 60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
| 120.24.1.gd.1 | $120$ | $5$ | $5$ | $1$ | $?$ |
| 120.60.5.dz.1 | $120$ | $2$ | $2$ | $5$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.240.17.ef.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.mn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.rd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.rn.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.eam.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.eao.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.ecx.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.edd.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fim.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fio.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fjr.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fjx.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fof.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.for.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fqa.1 | $120$ | $2$ | $2$ | $17$ |
| 120.240.17.fqm.1 | $120$ | $2$ | $2$ | $17$ |