Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-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 | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
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: | 8G0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&8\\71&21\end{bmatrix}$, $\begin{bmatrix}25&52\\19&63\end{bmatrix}$, $\begin{bmatrix}51&4\\16&55\end{bmatrix}$, $\begin{bmatrix}57&112\\8&77\end{bmatrix}$, $\begin{bmatrix}101&84\\68&29\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 40.24.0.v.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $737280$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 2 x^{2} + 5 y^{2} + 80 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 |
---|---|---|---|---|---|
12.24.0-4.d.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
120.24.0-4.d.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.96.1-40.dg.1.1 | $120$ | $2$ | $2$ | $1$ |
120.96.1-40.dh.1.2 | $120$ | $2$ | $2$ | $1$ |
120.96.1-40.di.1.4 | $120$ | $2$ | $2$ | $1$ |
120.96.1-40.dj.1.3 | $120$ | $2$ | $2$ | $1$ |
120.240.8-40.bo.1.8 | $120$ | $5$ | $5$ | $8$ |
120.288.7-40.cq.1.11 | $120$ | $6$ | $6$ | $7$ |
120.480.15-40.dm.1.10 | $120$ | $10$ | $10$ | $15$ |
120.96.1-120.ki.1.1 | $120$ | $2$ | $2$ | $1$ |
120.96.1-120.kj.1.4 | $120$ | $2$ | $2$ | $1$ |
120.96.1-120.kk.1.5 | $120$ | $2$ | $2$ | $1$ |
120.96.1-120.kl.1.5 | $120$ | $2$ | $2$ | $1$ |
120.144.4-120.fw.1.12 | $120$ | $3$ | $3$ | $4$ |
120.192.3-120.jg.1.8 | $120$ | $4$ | $4$ | $3$ |