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Properties

Label 120.144.5.ddf.1
Level $120$
Index $144$
Genus $5$
Cusps $16$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $20$ Newform level: $1$
Index: $144$ $\PSL_2$-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: $\begin{bmatrix}31&60\\93&61\end{bmatrix}$, $\begin{bmatrix}39&20\\31&109\end{bmatrix}$, $\begin{bmatrix}53&60\\117&19\end{bmatrix}$, $\begin{bmatrix}77&60\\53&41\end{bmatrix}$, $\begin{bmatrix}89&10\\41&11\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.288.5-120.ddf.1.1, 120.288.5-120.ddf.1.2, 120.288.5-120.ddf.1.3, 120.288.5-120.ddf.1.4, 120.288.5-120.ddf.1.5, 120.288.5-120.ddf.1.6, 120.288.5-120.ddf.1.7, 120.288.5-120.ddf.1.8, 120.288.5-120.ddf.1.9, 120.288.5-120.ddf.1.10, 120.288.5-120.ddf.1.11, 120.288.5-120.ddf.1.12, 120.288.5-120.ddf.1.13, 120.288.5-120.ddf.1.14, 120.288.5-120.ddf.1.15, 120.288.5-120.ddf.1.16
Cyclic 120-isogeny field degree: $16$
Cyclic 120-torsion field degree: $256$
Full 120-torsion field degree: $245760$

Rational points

This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
40.72.3.ee.2 $40$ $2$ $2$ $3$ $0$
60.72.1.cf.1 $60$ $2$ $2$ $1$ $1$
120.72.1.dh.2 $120$ $2$ $2$ $1$ $?$
120.72.1.mb.1 $120$ $2$ $2$ $1$ $?$
120.72.3.dmn.1 $120$ $2$ $2$ $3$ $?$
120.72.3.drb.1 $120$ $2$ $2$ $3$ $?$
120.72.3.edz.1 $120$ $2$ $2$ $3$ $?$