↑

Properties

Label 120.96.3.sn.4
Level $120$
Index $96$
Genus $3$
Cusps $12$
$\Q$-cusps $2$

Related objects

Downloads

Learn more

Invariants

Level: $120$ $\SL_2$-level: $24$ 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: $12$ (of which $2$ are rational) Cusp widths $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ Cusp orbits $1^{2}\cdot2^{5}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 3$
$\overline{\Q}$-gonality: $2 \le \gamma \le 3$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24W3

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}21&104\\8&45\end{bmatrix}$, $\begin{bmatrix}64&3\\81&58\end{bmatrix}$, $\begin{bmatrix}82&63\\63&46\end{bmatrix}$, $\begin{bmatrix}105&26\\64&11\end{bmatrix}$, $\begin{bmatrix}113&58\\60&79\end{bmatrix}$, $\begin{bmatrix}118&65\\13&54\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.3-120.sn.4.1, 120.192.3-120.sn.4.2, 120.192.3-120.sn.4.3, 120.192.3-120.sn.4.4, 120.192.3-120.sn.4.5, 120.192.3-120.sn.4.6, 120.192.3-120.sn.4.7, 120.192.3-120.sn.4.8, 120.192.3-120.sn.4.9, 120.192.3-120.sn.4.10, 120.192.3-120.sn.4.11, 120.192.3-120.sn.4.12, 120.192.3-120.sn.4.13, 120.192.3-120.sn.4.14, 120.192.3-120.sn.4.15, 120.192.3-120.sn.4.16, 120.192.3-120.sn.4.17, 120.192.3-120.sn.4.18, 120.192.3-120.sn.4.19, 120.192.3-120.sn.4.20, 120.192.3-120.sn.4.21, 120.192.3-120.sn.4.22, 120.192.3-120.sn.4.23, 120.192.3-120.sn.4.24, 120.192.3-120.sn.4.25, 120.192.3-120.sn.4.26, 120.192.3-120.sn.4.27, 120.192.3-120.sn.4.28, 120.192.3-120.sn.4.29, 120.192.3-120.sn.4.30, 120.192.3-120.sn.4.31, 120.192.3-120.sn.4.32
Cyclic 120-isogeny field degree: $12$
Cyclic 120-torsion field degree: $384$
Full 120-torsion field degree: $368640$

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
12.48.0.c.3 $12$ $2$ $2$ $0$ $0$
120.48.1.zx.1 $120$ $2$ $2$ $1$ $?$
120.48.2.h.2 $120$ $2$ $2$ $2$ $?$

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

Covering curve Level Index Degree Genus
120.192.5.ly.3 $120$ $2$ $2$ $5$
120.192.5.rh.3 $120$ $2$ $2$ $5$
120.192.5.ta.1 $120$ $2$ $2$ $5$
120.192.5.te.4 $120$ $2$ $2$ $5$
120.192.5.wq.3 $120$ $2$ $2$ $5$
120.192.5.xa.4 $120$ $2$ $2$ $5$
120.192.5.xs.2 $120$ $2$ $2$ $5$
120.192.5.xx.4 $120$ $2$ $2$ $5$
120.192.5.bab.3 $120$ $2$ $2$ $5$
120.192.5.bae.3 $120$ $2$ $2$ $5$
120.192.5.bak.3 $120$ $2$ $2$ $5$
120.192.5.bal.1 $120$ $2$ $2$ $5$
120.192.5.bbx.4 $120$ $2$ $2$ $5$
120.192.5.bca.4 $120$ $2$ $2$ $5$
120.192.5.bde.4 $120$ $2$ $2$ $5$
120.192.5.bdf.3 $120$ $2$ $2$ $5$
120.288.13.dts.1 $120$ $3$ $3$ $13$