Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $12^{4}\cdot24^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24U9 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&10\\20&53\end{bmatrix}$, $\begin{bmatrix}63&44\\112&117\end{bmatrix}$, $\begin{bmatrix}69&38\\56&93\end{bmatrix}$, $\begin{bmatrix}71&44\\88&119\end{bmatrix}$, $\begin{bmatrix}109&80\\112&91\end{bmatrix}$, $\begin{bmatrix}111&52\\56&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.9.bgc.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.5-24.p.1.32 | $24$ | $2$ | $2$ | $5$ | $1$ |
120.144.4-120.bm.1.50 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bm.1.107 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.10 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.123 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.5-24.p.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ |