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: | $\begin{bmatrix}31&76\\14&73\end{bmatrix}$, $\begin{bmatrix}53&58\\90&31\end{bmatrix}$, $\begin{bmatrix}59&114\\22&41\end{bmatrix}$, $\begin{bmatrix}70&47\\11&36\end{bmatrix}$, $\begin{bmatrix}106&103\\63&56\end{bmatrix}$ |
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 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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.36.0.a.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.36.1.bg.1 | $60$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.36.0.f.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.ef.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.jd.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.si.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.sm.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dbo.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dbq.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dcc.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.dce.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.edn.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.edo.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.efb.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.efc.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.ent.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.enu.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eoh.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.144.5.eoi.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.216.13.wq.1 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |
120.288.13.ifw.1 | $120$ | $4$ | $4$ | $13$ | $?$ | not computed |
120.360.13.fs.1 | $120$ | $5$ | $5$ | $13$ | $?$ | not computed |