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 | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-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: | $\begin{bmatrix}7&16\\0&17\end{bmatrix}$, $\begin{bmatrix}37&80\\62&59\end{bmatrix}$, $\begin{bmatrix}43&16\\68&57\end{bmatrix}$, $\begin{bmatrix}91&112\\52&63\end{bmatrix}$, $\begin{bmatrix}103&72\\102&79\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.48.0.ba.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $368640$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 8 x^{2} - 3 y^{2} - 3 z^{2} $ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.48.0-8.i.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 120.48.0-24.h.1.18 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-24.h.1.24 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-8.i.1.12 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-24.by.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-24.by.1.14 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.