Properties

Label 120.288.9-120.bfs.2.41
Level $120$
Index $288$
Genus $9$
Cusps $8$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $288$ $\PSL_2$-index:$144$
Genus: $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (none of which are rational) Cusp widths $12^{4}\cdot24^{4}$ Cusp orbits $2^{4}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 16$
$\overline{\Q}$-gonality: $2 \le \gamma \le 9$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24U9

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}39&10\\40&21\end{bmatrix}$, $\begin{bmatrix}73&94\\116&49\end{bmatrix}$, $\begin{bmatrix}79&94\\40&71\end{bmatrix}$, $\begin{bmatrix}99&112\\16&15\end{bmatrix}$, $\begin{bmatrix}113&40\\20&119\end{bmatrix}$, $\begin{bmatrix}117&40\\40&3\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.144.9.bfs.2 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $1536$
Full 120-torsion field degree: $122880$

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.144.5-24.o.1.32 $24$ $2$ $2$ $5$ $1$
120.144.4-120.bl.1.50 $120$ $2$ $2$ $4$ $?$
120.144.4-120.bl.1.103 $120$ $2$ $2$ $4$ $?$
120.144.4-120.bo.1.14 $120$ $2$ $2$ $4$ $?$
120.144.4-120.bo.1.123 $120$ $2$ $2$ $4$ $?$
120.144.5-24.o.1.12 $120$ $2$ $2$ $5$ $?$