Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $2^{2}$ | ||
| 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: | 4E0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}83&98\\113&15\end{bmatrix}$, $\begin{bmatrix}95&8\\1&119\end{bmatrix}$, $\begin{bmatrix}97&46\\93&65\end{bmatrix}$, $\begin{bmatrix}103&24\\16&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.12.0.m.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $1474560$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 8 x^{2} - 3 y^{2} - 192 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 |
|---|---|---|---|---|---|
| 40.12.0-4.b.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 120.12.0-4.b.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.72.2-24.bw.1.3 | $120$ | $3$ | $3$ | $2$ |
| 120.96.1-24.ie.1.11 | $120$ | $4$ | $4$ | $1$ |
| 120.120.4-120.y.1.3 | $120$ | $5$ | $5$ | $4$ |
| 120.144.3-120.bdw.1.6 | $120$ | $6$ | $6$ | $3$ |
| 120.240.7-120.bw.1.7 | $120$ | $10$ | $10$ | $7$ |