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 | $2^{3}\cdot4$ | ||
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: | 24H8 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}15&106\\32&75\end{bmatrix}$, $\begin{bmatrix}29&0\\96&41\end{bmatrix}$, $\begin{bmatrix}31&40\\112&87\end{bmatrix}$, $\begin{bmatrix}33&118\\32&39\end{bmatrix}$, $\begin{bmatrix}51&112\\52&35\end{bmatrix}$, $\begin{bmatrix}95&92\\32&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.8.hh.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $122880$ |
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 |
---|---|---|---|---|---|
24.144.4-24.x.1.50 | $24$ | $2$ | $2$ | $4$ | $0$ |
120.144.4-24.x.1.28 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bg.1.26 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bg.1.55 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.118 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.123 | $120$ | $2$ | $2$ | $4$ | $?$ |