Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 72$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20H1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}28&81\\97&92\end{bmatrix}$, $\begin{bmatrix}30&11\\97&14\end{bmatrix}$, $\begin{bmatrix}49&54\\68&55\end{bmatrix}$, $\begin{bmatrix}101&16\\94&63\end{bmatrix}$, $\begin{bmatrix}118&51\\91&8\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $512$ |
Full 120-torsion field degree: | $491520$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.36.0.d.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.36.1.bg.1 | $60$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.36.0.c.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.144.5.fd.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.iu.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.sw.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.sz.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dvr.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dvt.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dvy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dwa.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eea.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eec.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eew.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.efe.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.epx.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.epy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eqs.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eqt.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.216.13.zn.1 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |
120.288.13.igx.2 | $120$ | $4$ | $4$ | $13$ | $?$ | not computed |
120.360.13.hr.1 | $120$ | $5$ | $5$ | $13$ | $?$ | not computed |