Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 10B5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}29&96\\32&71\end{bmatrix}$, $\begin{bmatrix}35&98\\28&81\end{bmatrix}$, $\begin{bmatrix}51&10\\40&111\end{bmatrix}$, $\begin{bmatrix}83&12\\34&107\end{bmatrix}$, $\begin{bmatrix}87&22\\52&111\end{bmatrix}$, $\begin{bmatrix}91&6\\86&79\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.120.5.c.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $147456$ |
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 |
---|---|---|---|---|---|
40.120.3-10.a.1.2 | $40$ | $2$ | $2$ | $3$ | $0$ |
60.120.3-10.a.1.4 | $60$ | $2$ | $2$ | $3$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.