Properties

Label 120.384.7-120.nb.1.21
Level $120$
Index $384$
Genus $7$
Cusps $20$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $384$ $\PSL_2$-index:$192$
Genus: $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$
Cusps: $20$ (none of which are rational) Cusp widths $2^{4}\cdot4^{2}\cdot6^{4}\cdot8^{4}\cdot12^{2}\cdot24^{4}$ Cusp orbits $2^{6}\cdot4^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $3 \le \gamma \le 12$
$\overline{\Q}$-gonality: $3 \le \gamma \le 7$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24AI7

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}27&58\\80&13\end{bmatrix}$, $\begin{bmatrix}41&31\\8&27\end{bmatrix}$, $\begin{bmatrix}51&46\\64&117\end{bmatrix}$, $\begin{bmatrix}71&10\\72&109\end{bmatrix}$, $\begin{bmatrix}79&83\\16&15\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.192.7.nb.1 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $6$
Cyclic 120-torsion field degree: $192$
Full 120-torsion field degree: $92160$

Rational points

This modular curve has no $\Q_p$ points for $p=47$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.192.3-24.gf.1.15 $24$ $2$ $2$ $3$ $0$
120.96.0-120.ep.2.12 $120$ $4$ $4$ $0$ $?$
120.192.3-24.gf.1.30 $120$ $2$ $2$ $3$ $?$
120.192.3-120.pp.1.13 $120$ $2$ $2$ $3$ $?$
120.192.3-120.pp.1.20 $120$ $2$ $2$ $3$ $?$
120.192.3-120.rw.2.13 $120$ $2$ $2$ $3$ $?$
120.192.3-120.rw.2.46 $120$ $2$ $2$ $3$ $?$