Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{2}\cdot24^{4}$ | Cusp orbits | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24B8 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&12\\80&109\end{bmatrix}$, $\begin{bmatrix}21&98\\32&53\end{bmatrix}$, $\begin{bmatrix}31&64\\64&89\end{bmatrix}$, $\begin{bmatrix}89&40\\40&9\end{bmatrix}$, $\begin{bmatrix}107&80\\56&1\end{bmatrix}$, $\begin{bmatrix}113&12\\80&73\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.144.8.pi.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $24$ |
| Cyclic 120-torsion field degree: | $768$ |
| Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=31$, and therefore no 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(3)$ | $3$ | $96$ | $48$ | $0$ | $0$ |
| 40.96.0-40.bb.1.1 | $40$ | $3$ | $3$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
| 40.96.0-40.bb.1.1 | $40$ | $3$ | $3$ | $0$ | $0$ |
| 120.144.4-120.bi.1.66 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.bi.1.75 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-24.ch.1.9 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.om.2.23 | $120$ | $2$ | $2$ | $4$ | $?$ |
| 120.144.4-120.om.2.42 | $120$ | $2$ | $2$ | $4$ | $?$ |