Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8O0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&52\\78&113\end{bmatrix}$, $\begin{bmatrix}51&64\\94&7\end{bmatrix}$, $\begin{bmatrix}63&20\\46&21\end{bmatrix}$, $\begin{bmatrix}69&64\\76&79\end{bmatrix}$, $\begin{bmatrix}109&108\\38&113\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.bt.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
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 |
---|---|---|---|---|---|
24.48.0-24.i.1.21 | $24$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-24.i.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ |
40.48.0-40.h.2.5 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-40.h.2.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.x.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.x.1.38 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.192.1-120.o.2.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.s.2.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.cs.2.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.cw.2.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dw.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dx.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ee.2.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ef.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gk.1.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gl.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gs.1.4 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gt.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ha.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hb.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hi.1.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hj.1.2 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.me.1.42 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.gs.1.44 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.ci.2.4 | $120$ | $5$ | $5$ | $16$ |