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Properties

Label 120.96.5.jn.1
Level $120$
Index $96$
Genus $5$
Cusps $8$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (none of which are rational) Cusp widths $4^{2}\cdot8^{2}\cdot12^{2}\cdot24^{2}$ Cusp orbits $2^{4}$
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: 24K5

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}19&32\\4&63\end{bmatrix}$, $\begin{bmatrix}38&3\\63&62\end{bmatrix}$, $\begin{bmatrix}64&105\\99&16\end{bmatrix}$, $\begin{bmatrix}78&31\\119&34\end{bmatrix}$, $\begin{bmatrix}92&15\\107&76\end{bmatrix}$, $\begin{bmatrix}106&77\\31&114\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.5-120.jn.1.1, 120.192.5-120.jn.1.2, 120.192.5-120.jn.1.3, 120.192.5-120.jn.1.4, 120.192.5-120.jn.1.5, 120.192.5-120.jn.1.6, 120.192.5-120.jn.1.7, 120.192.5-120.jn.1.8, 120.192.5-120.jn.1.9, 120.192.5-120.jn.1.10, 120.192.5-120.jn.1.11, 120.192.5-120.jn.1.12, 120.192.5-120.jn.1.13, 120.192.5-120.jn.1.14, 120.192.5-120.jn.1.15, 120.192.5-120.jn.1.16, 120.192.5-120.jn.1.17, 120.192.5-120.jn.1.18, 120.192.5-120.jn.1.19, 120.192.5-120.jn.1.20, 120.192.5-120.jn.1.21, 120.192.5-120.jn.1.22, 120.192.5-120.jn.1.23, 120.192.5-120.jn.1.24, 120.192.5-120.jn.1.25, 120.192.5-120.jn.1.26, 120.192.5-120.jn.1.27, 120.192.5-120.jn.1.28, 120.192.5-120.jn.1.29, 120.192.5-120.jn.1.30, 120.192.5-120.jn.1.31, 120.192.5-120.jn.1.32
Cyclic 120-isogeny field degree: $24$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $368640$

Rational points

This modular curve has no $\Q_p$ points for $p=13$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.48.3.bv.1 $24$ $2$ $2$ $3$ $0$
60.48.2.f.1 $60$ $2$ $2$ $2$ $1$
120.24.1.gd.1 $120$ $4$ $4$ $1$ $?$
120.48.2.k.1 $120$ $2$ $2$ $2$ $?$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
120.192.9.gh.1 $120$ $2$ $2$ $9$
120.192.9.vz.1 $120$ $2$ $2$ $9$
120.192.9.bbb.1 $120$ $2$ $2$ $9$
120.192.9.bbv.1 $120$ $2$ $2$ $9$
120.192.9.cjh.1 $120$ $2$ $2$ $9$
120.192.9.cjj.1 $120$ $2$ $2$ $9$
120.192.9.cma.1 $120$ $2$ $2$ $9$
120.192.9.cmg.1 $120$ $2$ $2$ $9$
120.192.9.cuz.1 $120$ $2$ $2$ $9$
120.192.9.cvb.1 $120$ $2$ $2$ $9$
120.192.9.cwe.1 $120$ $2$ $2$ $9$
120.192.9.cwk.1 $120$ $2$ $2$ $9$
120.192.9.cys.1 $120$ $2$ $2$ $9$
120.192.9.cze.1 $120$ $2$ $2$ $9$
120.192.9.czx.1 $120$ $2$ $2$ $9$
120.192.9.daj.1 $120$ $2$ $2$ $9$
120.288.17.ccuw.1 $120$ $3$ $3$ $17$