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 | $4^{8}\cdot8^{2}$ | 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: | 8N0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&90\\56&19\end{bmatrix}$, $\begin{bmatrix}47&102\\36&53\end{bmatrix}$, $\begin{bmatrix}77&64\\4&75\end{bmatrix}$, $\begin{bmatrix}101&100\\60&17\end{bmatrix}$, $\begin{bmatrix}115&38\\76&57\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.h.1 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 |
---|---|---|---|---|---|
12.48.0-12.c.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-12.c.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
40.48.0-40.h.2.30 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-40.h.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.u.2.19 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.u.2.61 | $120$ | $2$ | $2$ | $0$ | $?$ |
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.q.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.cb.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dc.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dg.1.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.fq.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gc.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gg.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gs.1.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ic.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.io.1.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.is.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.je.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ko.2.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ks.1.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.kw.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ky.2.7 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.ba.2.49 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.v.2.4 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.p.1.30 | $120$ | $5$ | $5$ | $16$ |