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Properties

Label 120.144.8.hz.1
Level $120$
Index $144$
Genus $8$
Cusps $10$
$\Q$-cusps $2$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $144$ $\PSL_2$-index:$144$
Genus: $8 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps: $10$ (of which $2$ are rational) Cusp widths $6^{4}\cdot12^{2}\cdot24^{4}$ Cusp orbits $1^{2}\cdot2^{2}\cdot4$
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: $3 \le \gamma \le 8$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24H8

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}7&52\\16&77\end{bmatrix}$, $\begin{bmatrix}9&56\\8&61\end{bmatrix}$, $\begin{bmatrix}15&32\\68&85\end{bmatrix}$, $\begin{bmatrix}15&44\\88&87\end{bmatrix}$, $\begin{bmatrix}17&20\\116&57\end{bmatrix}$, $\begin{bmatrix}63&76\\88&47\end{bmatrix}$, $\begin{bmatrix}73&10\\40&87\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.288.8-120.hz.1.1, 120.288.8-120.hz.1.2, 120.288.8-120.hz.1.3, 120.288.8-120.hz.1.4, 120.288.8-120.hz.1.5, 120.288.8-120.hz.1.6, 120.288.8-120.hz.1.7, 120.288.8-120.hz.1.8, 120.288.8-120.hz.1.9, 120.288.8-120.hz.1.10, 120.288.8-120.hz.1.11, 120.288.8-120.hz.1.12, 120.288.8-120.hz.1.13, 120.288.8-120.hz.1.14, 120.288.8-120.hz.1.15, 120.288.8-120.hz.1.16, 120.288.8-120.hz.1.17, 120.288.8-120.hz.1.18, 120.288.8-120.hz.1.19, 120.288.8-120.hz.1.20, 120.288.8-120.hz.1.21, 120.288.8-120.hz.1.22, 120.288.8-120.hz.1.23, 120.288.8-120.hz.1.24, 120.288.8-120.hz.1.25, 120.288.8-120.hz.1.26, 120.288.8-120.hz.1.27, 120.288.8-120.hz.1.28, 120.288.8-120.hz.1.29, 120.288.8-120.hz.1.30, 120.288.8-120.hz.1.31, 120.288.8-120.hz.1.32, 120.288.8-120.hz.1.33, 120.288.8-120.hz.1.34, 120.288.8-120.hz.1.35, 120.288.8-120.hz.1.36, 120.288.8-120.hz.1.37, 120.288.8-120.hz.1.38, 120.288.8-120.hz.1.39, 120.288.8-120.hz.1.40, 120.288.8-120.hz.1.41, 120.288.8-120.hz.1.42, 120.288.8-120.hz.1.43, 120.288.8-120.hz.1.44, 120.288.8-120.hz.1.45, 120.288.8-120.hz.1.46, 120.288.8-120.hz.1.47, 120.288.8-120.hz.1.48, 120.288.8-120.hz.1.49, 120.288.8-120.hz.1.50, 120.288.8-120.hz.1.51, 120.288.8-120.hz.1.52, 120.288.8-120.hz.1.53, 120.288.8-120.hz.1.54, 120.288.8-120.hz.1.55, 120.288.8-120.hz.1.56, 120.288.8-120.hz.1.57, 120.288.8-120.hz.1.58, 120.288.8-120.hz.1.59, 120.288.8-120.hz.1.60, 120.288.8-120.hz.1.61, 120.288.8-120.hz.1.62, 120.288.8-120.hz.1.63, 120.288.8-120.hz.1.64
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $245760$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
24.72.4.z.1 $24$ $2$ $2$ $4$ $0$
120.72.4.bh.1 $120$ $2$ $2$ $4$ $?$
120.72.4.bm.1 $120$ $2$ $2$ $4$ $?$

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

Covering curve Level Index Degree Genus
120.288.15.cdg.1 $120$ $2$ $2$ $15$
120.288.15.ceg.1 $120$ $2$ $2$ $15$
120.288.15.cha.1 $120$ $2$ $2$ $15$
120.288.15.chw.1 $120$ $2$ $2$ $15$
120.288.15.ctr.1 $120$ $2$ $2$ $15$
120.288.15.cuw.1 $120$ $2$ $2$ $15$
120.288.15.cxq.1 $120$ $2$ $2$ $15$
120.288.15.cym.1 $120$ $2$ $2$ $15$
120.288.15.dgc.1 $120$ $2$ $2$ $15$
120.288.15.dhc.1 $120$ $2$ $2$ $15$
120.288.15.djw.1 $120$ $2$ $2$ $15$
120.288.15.dks.1 $120$ $2$ $2$ $15$
120.288.15.doy.1 $120$ $2$ $2$ $15$
120.288.15.dqi.1 $120$ $2$ $2$ $15$
120.288.15.drg.1 $120$ $2$ $2$ $15$
120.288.15.dsa.1 $120$ $2$ $2$ $15$
120.288.17.btv.1 $120$ $2$ $2$ $17$
120.288.17.buc.1 $120$ $2$ $2$ $17$
120.288.17.caa.2 $120$ $2$ $2$ $17$
120.288.17.cah.1 $120$ $2$ $2$ $17$
120.288.17.chw.1 $120$ $2$ $2$ $17$
120.288.17.chx.2 $120$ $2$ $2$ $17$
120.288.17.cik.1 $120$ $2$ $2$ $17$
120.288.17.cil.1 $120$ $2$ $2$ $17$
120.288.17.fdo.2 $120$ $2$ $2$ $17$
120.288.17.fdp.1 $120$ $2$ $2$ $17$
120.288.17.fdy.1 $120$ $2$ $2$ $17$
120.288.17.fdz.1 $120$ $2$ $2$ $17$
120.288.17.fhg.1 $120$ $2$ $2$ $17$
120.288.17.fhh.1 $120$ $2$ $2$ $17$
120.288.17.fhq.1 $120$ $2$ $2$ $17$
120.288.17.fhr.2 $120$ $2$ $2$ $17$
120.288.17.icg.2 $120$ $2$ $2$ $17$
120.288.17.ich.1 $120$ $2$ $2$ $17$
120.288.17.icm.2 $120$ $2$ $2$ $17$
120.288.17.icn.2 $120$ $2$ $2$ $17$
120.288.17.ify.2 $120$ $2$ $2$ $17$
120.288.17.ifz.2 $120$ $2$ $2$ $17$
120.288.17.ige.1 $120$ $2$ $2$ $17$
120.288.17.igf.2 $120$ $2$ $2$ $17$
120.288.17.jho.2 $120$ $2$ $2$ $17$
120.288.17.jhp.2 $120$ $2$ $2$ $17$
120.288.17.jhq.2 $120$ $2$ $2$ $17$
120.288.17.jhr.1 $120$ $2$ $2$ $17$
120.288.17.jlg.1 $120$ $2$ $2$ $17$
120.288.17.jlh.2 $120$ $2$ $2$ $17$
120.288.17.jli.2 $120$ $2$ $2$ $17$
120.288.17.jlj.2 $120$ $2$ $2$ $17$