Invariants
Level: | $120$ | $\SL_2$-level: | $60$ | 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 | $1^{2}\cdot2^{2}\cdot3^{2}\cdot5^{2}\cdot6^{2}\cdot10^{2}\cdot15^{2}\cdot30^{2}$ | Cusp orbits | $2^{8}$ | ||
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: | 30S5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&6\\0&89\end{bmatrix}$, $\begin{bmatrix}29&42\\86&55\end{bmatrix}$, $\begin{bmatrix}32&105\\93&14\end{bmatrix}$, $\begin{bmatrix}47&34\\50&21\end{bmatrix}$, $\begin{bmatrix}75&68\\4&59\end{bmatrix}$, $\begin{bmatrix}95&84\\32&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.5.ebg.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $4$ |
Cyclic 120-torsion field degree: | $128$ |
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 |
---|---|---|---|---|---|
60.144.3-30.a.1.9 | $60$ | $2$ | $2$ | $3$ | $0$ |
120.144.3-30.a.1.25 | $120$ | $2$ | $2$ | $3$ | $?$ |