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 | $2^{5}$ | ||
| 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: | 8N0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}17&48\\8&29\end{bmatrix}$, $\begin{bmatrix}55&2\\64&61\end{bmatrix}$, $\begin{bmatrix}63&94\\76&51\end{bmatrix}$, $\begin{bmatrix}79&36\\116&47\end{bmatrix}$, $\begin{bmatrix}87&2\\56&83\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.0.be.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $368640$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 24.48.0-8.e.2.3 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 40.48.0-8.e.2.15 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 60.48.0-60.c.1.4 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 120.48.0-60.c.1.10 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.t.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
| 120.48.0-120.t.1.55 | $120$ | $2$ | $2$ | $0$ | $?$ |
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.be.1.6 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.da.2.12 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.dy.2.4 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.eg.1.6 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.iz.1.12 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.jh.2.10 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.jo.2.2 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.jw.1.12 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.mu.2.2 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.nc.1.12 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.nl.1.12 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.nt.2.10 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.pg.2.4 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.po.1.6 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.pt.1.6 | $120$ | $2$ | $2$ | $1$ |
| 120.192.1-120.px.2.12 | $120$ | $2$ | $2$ | $1$ |
| 120.288.8-120.dn.1.63 | $120$ | $3$ | $3$ | $8$ |
| 120.384.7-120.dj.2.17 | $120$ | $4$ | $4$ | $7$ |
| 120.480.16-120.bt.1.9 | $120$ | $5$ | $5$ | $16$ |