Invariants
| Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{4}\cdot40^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40A17 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}59&26\\58&53\end{bmatrix}$, $\begin{bmatrix}77&33\\30&71\end{bmatrix}$, $\begin{bmatrix}99&106\\40&67\end{bmatrix}$, $\begin{bmatrix}119&61\\104&65\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $48$ |
| Cyclic 120-torsion field degree: | $1536$ |
| Full 120-torsion field degree: | $147456$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $48$ | $48$ | $0$ | $0$ |
| 24.48.1.cq.1 | $24$ | $5$ | $5$ | $1$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.48.1.cq.1 | $24$ | $5$ | $5$ | $1$ | $1$ |
| 40.120.8.bh.1 | $40$ | $2$ | $2$ | $8$ | $4$ |
| 120.120.8.bu.1 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.120.8.qv.1 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.120.8.sz.1 | $120$ | $2$ | $2$ | $8$ | $?$ |
| 120.120.9.j.1 | $120$ | $2$ | $2$ | $9$ | $?$ |
| 120.120.9.qd.1 | $120$ | $2$ | $2$ | $9$ | $?$ |
| 120.120.9.sh.1 | $120$ | $2$ | $2$ | $9$ | $?$ |