Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
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: | 20I5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&60\\19&29\end{bmatrix}$, $\begin{bmatrix}23&100\\9&11\end{bmatrix}$, $\begin{bmatrix}53&10\\43&31\end{bmatrix}$, $\begin{bmatrix}119&110\\27&11\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.5.bor.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $256$ |
Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.144.1-40.n.2.11 | $40$ | $2$ | $2$ | $1$ | $0$ |
60.144.1-60.cf.1.15 | $60$ | $2$ | $2$ | $1$ | $1$ |
120.144.1-40.n.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.144.1-60.cf.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.144.3-120.fse.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.3-120.fse.2.15 | $120$ | $2$ | $2$ | $3$ | $?$ |