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: | $\begin{bmatrix}9&52\\40&97\end{bmatrix}$, $\begin{bmatrix}41&24\\32&1\end{bmatrix}$, $\begin{bmatrix}89&88\\40&93\end{bmatrix}$, $\begin{bmatrix}107&10\\40&69\end{bmatrix}$, $\begin{bmatrix}107&100\\112&81\end{bmatrix}$, $\begin{bmatrix}119&94\\64&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.8.pj.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 $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
120.96.0-120.cy.1.4 | $120$ | $3$ | $3$ | $0$ | $?$ |
120.144.4-120.bj.1.99 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bj.1.105 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-24.ch.1.15 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.on.2.23 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.on.2.42 | $120$ | $2$ | $2$ | $4$ | $?$ |