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: | $\begin{bmatrix}1&32\\28&27\end{bmatrix}$, $\begin{bmatrix}79&112\\60&31\end{bmatrix}$, $\begin{bmatrix}91&40\\68&21\end{bmatrix}$, $\begin{bmatrix}93&62\\4&35\end{bmatrix}$, $\begin{bmatrix}111&100\\40&31\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 40.48.0.i.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 3 x^{2} - 4 x y + 3 y^{2} + 10 z^{2} $ |
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 |
---|---|---|---|---|---|
24.48.0-8.d.2.9 | $24$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-20.c.1.14 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-20.c.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-8.d.2.7 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-40.h.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-40.h.1.21 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.192.1-40.c.2.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.i.1.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.ba.1.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.bc.2.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.bs.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.bu.2.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.ca.2.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-40.cb.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.fr.2.14 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.fv.2.12 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gw.2.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ha.2.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ly.2.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.mc.2.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ne.2.14 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ni.2.15 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.bw.1.53 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.cf.1.22 | $120$ | $4$ | $4$ | $7$ |
120.480.16-40.o.1.7 | $120$ | $5$ | $5$ | $16$ |