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Properties

Label 120.48.2.h.2
Level $120$
Index $48$
Genus $2$
Cusps $6$
$\Q$-cusps $6$

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Invariants

Level: $120$ $\SL_2$-level: $24$ Newform level: $1$
Index: $48$ $\PSL_2$-index:$48$
Genus: $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (all of which are rational) Cusp widths $2^{2}\cdot6^{2}\cdot8\cdot24$ Cusp orbits $1^{6}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $6$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24F2

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}9&80\\116&9\end{bmatrix}$, $\begin{bmatrix}15&16\\2&61\end{bmatrix}$, $\begin{bmatrix}33&22\\116&31\end{bmatrix}$, $\begin{bmatrix}61&30\\30&1\end{bmatrix}$, $\begin{bmatrix}83&66\\8&85\end{bmatrix}$, $\begin{bmatrix}108&79\\79&36\end{bmatrix}$, $\begin{bmatrix}115&36\\102&13\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.96.2-120.h.2.1, 120.96.2-120.h.2.2, 120.96.2-120.h.2.3, 120.96.2-120.h.2.4, 120.96.2-120.h.2.5, 120.96.2-120.h.2.6, 120.96.2-120.h.2.7, 120.96.2-120.h.2.8, 120.96.2-120.h.2.9, 120.96.2-120.h.2.10, 120.96.2-120.h.2.11, 120.96.2-120.h.2.12, 120.96.2-120.h.2.13, 120.96.2-120.h.2.14, 120.96.2-120.h.2.15, 120.96.2-120.h.2.16, 120.96.2-120.h.2.17, 120.96.2-120.h.2.18, 120.96.2-120.h.2.19, 120.96.2-120.h.2.20, 120.96.2-120.h.2.21, 120.96.2-120.h.2.22, 120.96.2-120.h.2.23, 120.96.2-120.h.2.24, 120.96.2-120.h.2.25, 120.96.2-120.h.2.26, 120.96.2-120.h.2.27, 120.96.2-120.h.2.28, 120.96.2-120.h.2.29, 120.96.2-120.h.2.30, 120.96.2-120.h.2.31, 120.96.2-120.h.2.32, 120.96.2-120.h.2.33, 120.96.2-120.h.2.34, 120.96.2-120.h.2.35, 120.96.2-120.h.2.36, 120.96.2-120.h.2.37, 120.96.2-120.h.2.38, 120.96.2-120.h.2.39, 120.96.2-120.h.2.40, 120.96.2-120.h.2.41, 120.96.2-120.h.2.42, 120.96.2-120.h.2.43, 120.96.2-120.h.2.44, 120.96.2-120.h.2.45, 120.96.2-120.h.2.46, 120.96.2-120.h.2.47, 120.96.2-120.h.2.48, 120.96.2-120.h.2.49, 120.96.2-120.h.2.50, 120.96.2-120.h.2.51, 120.96.2-120.h.2.52, 120.96.2-120.h.2.53, 120.96.2-120.h.2.54, 120.96.2-120.h.2.55, 120.96.2-120.h.2.56, 120.96.2-120.h.2.57, 120.96.2-120.h.2.58, 120.96.2-120.h.2.59, 120.96.2-120.h.2.60, 120.96.2-120.h.2.61, 120.96.2-120.h.2.62, 120.96.2-120.h.2.63, 120.96.2-120.h.2.64
Cyclic 120-isogeny field degree: $12$
Cyclic 120-torsion field degree: $384$
Full 120-torsion field degree: $737280$

Rational points

This modular curve has 6 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
$X_0(12)$ $12$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
120.96.3.eq.1 $120$ $2$ $2$ $3$
120.96.3.hp.1 $120$ $2$ $2$ $3$
120.96.3.kh.1 $120$ $2$ $2$ $3$
120.96.3.kk.1 $120$ $2$ $2$ $3$
120.96.3.ly.2 $120$ $2$ $2$ $3$
120.96.3.ma.2 $120$ $2$ $2$ $3$
120.96.3.mk.2 $120$ $2$ $2$ $3$
120.96.3.mm.2 $120$ $2$ $2$ $3$
120.96.3.nb.1 $120$ $2$ $2$ $3$
120.96.3.nc.1 $120$ $2$ $2$ $3$
120.96.3.nf.1 $120$ $2$ $2$ $3$
120.96.3.ng.1 $120$ $2$ $2$ $3$
120.96.3.nr.2 $120$ $2$ $2$ $3$
120.96.3.ns.2 $120$ $2$ $2$ $3$
120.96.3.nv.2 $120$ $2$ $2$ $3$
120.96.3.nw.2 $120$ $2$ $2$ $3$
120.96.3.sa.2 $120$ $2$ $2$ $3$
120.96.3.sa.4 $120$ $2$ $2$ $3$
120.96.3.sb.2 $120$ $2$ $2$ $3$
120.96.3.sb.4 $120$ $2$ $2$ $3$
120.96.3.se.2 $120$ $2$ $2$ $3$
120.96.3.se.4 $120$ $2$ $2$ $3$
120.96.3.sf.2 $120$ $2$ $2$ $3$
120.96.3.sf.4 $120$ $2$ $2$ $3$
120.96.3.si.2 $120$ $2$ $2$ $3$
120.96.3.si.4 $120$ $2$ $2$ $3$
120.96.3.sj.2 $120$ $2$ $2$ $3$
120.96.3.sj.4 $120$ $2$ $2$ $3$
120.96.3.sm.2 $120$ $2$ $2$ $3$
120.96.3.sm.4 $120$ $2$ $2$ $3$
120.96.3.sn.2 $120$ $2$ $2$ $3$
120.96.3.sn.4 $120$ $2$ $2$ $3$
120.96.3.sq.2 $120$ $2$ $2$ $3$
120.96.3.sq.4 $120$ $2$ $2$ $3$
120.96.3.sr.2 $120$ $2$ $2$ $3$
120.96.3.sr.4 $120$ $2$ $2$ $3$
120.96.3.su.2 $120$ $2$ $2$ $3$
120.96.3.su.4 $120$ $2$ $2$ $3$
120.96.3.sv.2 $120$ $2$ $2$ $3$
120.96.3.sv.4 $120$ $2$ $2$ $3$
120.96.3.sy.2 $120$ $2$ $2$ $3$
120.96.3.sy.4 $120$ $2$ $2$ $3$
120.96.3.sz.2 $120$ $2$ $2$ $3$
120.96.3.sz.4 $120$ $2$ $2$ $3$
120.96.3.tc.2 $120$ $2$ $2$ $3$
120.96.3.tc.4 $120$ $2$ $2$ $3$
120.96.3.td.2 $120$ $2$ $2$ $3$
120.96.3.td.4 $120$ $2$ $2$ $3$
120.144.7.dkk.1 $120$ $3$ $3$ $7$
120.240.18.k.1 $120$ $5$ $5$ $18$
120.288.19.bfb.2 $120$ $6$ $6$ $19$