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: | $\begin{bmatrix}43&76\\40&51\end{bmatrix}$, $\begin{bmatrix}54&113\\55&38\end{bmatrix}$, $\begin{bmatrix}62&5\\49&66\end{bmatrix}$, $\begin{bmatrix}89&98\\42&71\end{bmatrix}$, $\begin{bmatrix}92&33\\87&80\end{bmatrix}$ |
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 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 |
---|---|---|---|---|---|
40.60.5.h.1 | $40$ | $2$ | $2$ | $5$ | $2$ |
60.60.4.cj.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
120.24.1.kp.1 | $120$ | $5$ | $5$ | $1$ | $?$ |
120.60.4.gn.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.ha.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.mb.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.pn.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.qb.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dvk.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dvq.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dxf.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.dxp.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jkq.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jky.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jlh.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jlp.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jon.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.joz.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jpc.1 | $120$ | $2$ | $2$ | $17$ |
120.240.17.jpo.1 | $120$ | $2$ | $2$ | $17$ |