Properties

Label 120.288.5-120.cov.1.15
Level $120$
Index $288$
Genus $5$
Cusps $16$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $20$ 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 $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ Cusp orbits $2^{4}\cdot4^{2}$
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: 20I5

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}37&10\\34&51\end{bmatrix}$, $\begin{bmatrix}41&20\\3&119\end{bmatrix}$, $\begin{bmatrix}57&50\\19&69\end{bmatrix}$, $\begin{bmatrix}73&20\\69&109\end{bmatrix}$
Contains $-I$: no $\quad$ (see 120.144.5.cov.1 for the level structure with $-I$)
Cyclic 120-isogeny field degree: $16$
Cyclic 120-torsion field degree: $256$
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
40.144.1-40.bf.1.3 $40$ $2$ $2$ $1$ $1$
60.144.3-60.xw.2.15 $60$ $2$ $2$ $3$ $0$
120.144.1-40.bf.1.9 $120$ $2$ $2$ $1$ $?$
120.144.1-120.dn.2.21 $120$ $2$ $2$ $1$ $?$
120.144.1-120.dn.2.30 $120$ $2$ $2$ $1$ $?$
120.144.3-60.xw.2.14 $120$ $2$ $2$ $3$ $?$