Invariants
Level: | $120$ | $\SL_2$-level: | $60$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $13 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $5^{4}\cdot10^{4}\cdot15^{4}\cdot30^{4}$ | Cusp orbits | $4^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 13$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 30N13 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}11&106\\74&27\end{bmatrix}$, $\begin{bmatrix}13&0\\58&77\end{bmatrix}$, $\begin{bmatrix}62&49\\21&28\end{bmatrix}$, $\begin{bmatrix}92&1\\39&58\end{bmatrix}$, $\begin{bmatrix}101&78\\84&29\end{bmatrix}$, $\begin{bmatrix}112&33\\45&88\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.13.dvz.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7,29$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ |
120.240.7-30.h.1.23 | $120$ | $2$ | $2$ | $7$ | $?$ |