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Properties

Label 120.96.3.wp.1
Level $120$
Index $96$
Genus $3$
Cusps $12$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $12$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (none of which are rational) Cusp widths $4^{6}\cdot12^{6}$ Cusp orbits $2^{2}\cdot4^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 4$
$\overline{\Q}$-gonality: $2 \le \gamma \le 3$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 12K3

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}31&102\\18&13\end{bmatrix}$, $\begin{bmatrix}43&34\\66&95\end{bmatrix}$, $\begin{bmatrix}59&12\\88&61\end{bmatrix}$, $\begin{bmatrix}94&73\\17&42\end{bmatrix}$, $\begin{bmatrix}105&88\\64&15\end{bmatrix}$, $\begin{bmatrix}108&61\\29&56\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.3-120.wp.1.1, 120.192.3-120.wp.1.2, 120.192.3-120.wp.1.3, 120.192.3-120.wp.1.4, 120.192.3-120.wp.1.5, 120.192.3-120.wp.1.6, 120.192.3-120.wp.1.7, 120.192.3-120.wp.1.8, 120.192.3-120.wp.1.9, 120.192.3-120.wp.1.10, 120.192.3-120.wp.1.11, 120.192.3-120.wp.1.12, 120.192.3-120.wp.1.13, 120.192.3-120.wp.1.14, 120.192.3-120.wp.1.15, 120.192.3-120.wp.1.16, 120.192.3-120.wp.1.17, 120.192.3-120.wp.1.18, 120.192.3-120.wp.1.19, 120.192.3-120.wp.1.20, 120.192.3-120.wp.1.21, 120.192.3-120.wp.1.22, 120.192.3-120.wp.1.23, 120.192.3-120.wp.1.24, 120.192.3-120.wp.1.25, 120.192.3-120.wp.1.26, 120.192.3-120.wp.1.27, 120.192.3-120.wp.1.28, 120.192.3-120.wp.1.29, 120.192.3-120.wp.1.30, 120.192.3-120.wp.1.31, 120.192.3-120.wp.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 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
24.48.2.o.1 $24$ $2$ $2$ $2$ $1$
60.48.2.f.1 $60$ $2$ $2$ $2$ $1$
120.24.0.gh.1 $120$ $4$ $4$ $0$ $?$
120.48.1.bzq.1 $120$ $2$ $2$ $1$ $?$

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

Covering curve Level Index Degree Genus
120.192.9.brb.1 $120$ $2$ $2$ $9$
120.192.9.brh.1 $120$ $2$ $2$ $9$
120.192.9.bsf.1 $120$ $2$ $2$ $9$
120.192.9.bsp.1 $120$ $2$ $2$ $9$
120.192.9.cio.1 $120$ $2$ $2$ $9$
120.192.9.ciu.1 $120$ $2$ $2$ $9$
120.192.9.clw.1 $120$ $2$ $2$ $9$
120.192.9.cmg.1 $120$ $2$ $2$ $9$
120.192.9.ddc.1 $120$ $2$ $2$ $9$
120.192.9.ddm.1 $120$ $2$ $2$ $9$
120.192.9.dgo.1 $120$ $2$ $2$ $9$
120.192.9.dgu.1 $120$ $2$ $2$ $9$
120.192.9.dpm.1 $120$ $2$ $2$ $9$
120.192.9.dpw.1 $120$ $2$ $2$ $9$
120.192.9.dqu.1 $120$ $2$ $2$ $9$
120.192.9.dra.1 $120$ $2$ $2$ $9$
120.288.13.gfc.1 $120$ $3$ $3$ $13$