Invariants
Level: | $120$ | $\SL_2$-level: | $4$ | ||||
Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4G0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}0&79\\59&112\end{bmatrix}$, $\begin{bmatrix}2&119\\93&110\end{bmatrix}$, $\begin{bmatrix}56&55\\113&32\end{bmatrix}$, $\begin{bmatrix}57&22\\110&89\end{bmatrix}$, $\begin{bmatrix}116&115\\81&56\end{bmatrix}$ |
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: | $1474560$ |
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 |
---|---|---|---|---|---|
24.12.0.bs.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.12.0.bn.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.48.1.si.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.so.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.tm.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.tw.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bgu.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bha.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bkk.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.bku.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cbe.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cbo.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cey.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cfe.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cli.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cls.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cmq.1 | $120$ | $2$ | $2$ | $1$ |
120.48.1.cmw.1 | $120$ | $2$ | $2$ | $1$ |
120.72.4.bbv.1 | $120$ | $3$ | $3$ | $4$ |
120.96.3.xh.1 | $120$ | $4$ | $4$ | $3$ |
120.120.8.kn.1 | $120$ | $5$ | $5$ | $8$ |
120.144.7.hoi.1 | $120$ | $6$ | $6$ | $7$ |
120.240.15.boz.1 | $120$ | $10$ | $10$ | $15$ |