Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8F1 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&92\\116&55\end{bmatrix}$, $\begin{bmatrix}47&50\\56&13\end{bmatrix}$, $\begin{bmatrix}49&92\\31&99\end{bmatrix}$, $\begin{bmatrix}103&52\\96&71\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.48.1.hc.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $368640$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.48.0-8.n.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 40.48.0-8.n.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 120.288.9-120.brj.1.10 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 120.384.9-120.ud.1.13 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
| 120.480.17-120.kp.1.8 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |