Invariants
| Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{6}\cdot6^{4}\cdot8^{2}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{8}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AB5 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&36\\38&115\end{bmatrix}$, $\begin{bmatrix}7&72\\24&97\end{bmatrix}$, $\begin{bmatrix}23&36\\108&73\end{bmatrix}$, $\begin{bmatrix}31&24\\118&61\end{bmatrix}$, $\begin{bmatrix}49&24\\72&13\end{bmatrix}$, $\begin{bmatrix}89&24\\32&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.192.5.nm.4 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $12$ |
| Cyclic 120-torsion field degree: | $192$ |
| Full 120-torsion field degree: | $92160$ |
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 |
|---|---|---|---|---|---|
| $X_1(3)$ | $3$ | $48$ | $48$ | $0$ | $0$ |
| 40.48.0-8.e.1.9 | $40$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.192.3-24.bq.2.62 | $24$ | $2$ | $2$ | $3$ | $0$ |
| 60.192.1-60.b.4.4 | $60$ | $2$ | $2$ | $1$ | $0$ |
| 120.192.1-60.b.4.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
| 120.192.3-24.bq.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ex.1.98 | $120$ | $2$ | $2$ | $3$ | $?$ |
| 120.192.3-120.ex.1.127 | $120$ | $2$ | $2$ | $3$ | $?$ |