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: | $\begin{bmatrix}38&9\\67&34\end{bmatrix}$, $\begin{bmatrix}41&34\\70&73\end{bmatrix}$, $\begin{bmatrix}93&64\\92&73\end{bmatrix}$, $\begin{bmatrix}97&76\\88&107\end{bmatrix}$, $\begin{bmatrix}108&73\\5&52\end{bmatrix}$ |
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 real points, 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.cq.1 | $40$ | $2$ | $2$ | $4$ | $2$ |
60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
120.24.1.gz.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.mh.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.ur.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.vf.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dzx.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dzz.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.eec.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.eei.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fjd.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fjf.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fkw.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.flc.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fot.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fpf.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fqo.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.fra.1 | $120$ | $2$ | $2$ | $17$ |