Modular curve 140.72.3.o.1

• Label: 140.72.3.o.1
• Level: $140$
• Index: $72$
• Genus: $3$
• Cusps: $8$
• $\Q$-cusps: $4$

Invariants

Level:	$140$		$\SL_2$-level:	$20$		Newform level:	$1$
Index:	$72$		$\PSL_2$-index:	$72$
Genus:	$3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps:	$8$ (of which $4$ are rational)		Cusp widths	$2^{2}\cdot4^{2}\cdot10^{2}\cdot20^{2}$		Cusp orbits	$1^{4}\cdot2^{2}$
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:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

20J3

Level structure

$\GL_2(\Z/140\Z)$-generators:	$\begin{bmatrix}21&80\\69&37\end{bmatrix}$, $\begin{bmatrix}27&120\\13&107\end{bmatrix}$, $\begin{bmatrix}37&40\\70&57\end{bmatrix}$, $\begin{bmatrix}97&120\\129&127\end{bmatrix}$, $\begin{bmatrix}119&120\\34&93\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	140.144.3-140.o.1.1, 140.144.3-140.o.1.2, 140.144.3-140.o.1.3, 140.144.3-140.o.1.4, 140.144.3-140.o.1.5, 140.144.3-140.o.1.6, 140.144.3-140.o.1.7, 140.144.3-140.o.1.8, 280.144.3-140.o.1.1, 280.144.3-140.o.1.2, 280.144.3-140.o.1.3, 280.144.3-140.o.1.4, 280.144.3-140.o.1.5, 280.144.3-140.o.1.6, 280.144.3-140.o.1.7, 280.144.3-140.o.1.8, 280.144.3-140.o.1.9, 280.144.3-140.o.1.10, 280.144.3-140.o.1.11, 280.144.3-140.o.1.12, 280.144.3-140.o.1.13, 280.144.3-140.o.1.14, 280.144.3-140.o.1.15, 280.144.3-140.o.1.16, 280.144.3-140.o.1.17, 280.144.3-140.o.1.18, 280.144.3-140.o.1.19, 280.144.3-140.o.1.20, 280.144.3-140.o.1.21, 280.144.3-140.o.1.22, 280.144.3-140.o.1.23, 280.144.3-140.o.1.24
Cyclic 140-isogeny field degree:	$8$
Cyclic 140-torsion field degree:	$384$
Full 140-torsion field degree:	$1290240$

Rational points

This modular curve has 4 rational cusps but no known non-cuspidal rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
$X_0(5)$	$5$	$12$	$12$	$0$	$0$
28.12.0.g.1	$28$	$6$	$6$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
$X_0(20)$	$20$	$2$	$2$	$1$	$0$
28.12.0.g.1	$28$	$6$	$6$	$0$	$0$
70.36.1.b.1	$70$	$2$	$2$	$1$	$0$
140.36.1.i.1	$140$	$2$	$2$	$1$	$?$

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

Covering curve	Level	Index	Degree	Genus
140.144.5.ci.1	$140$	$2$	$2$	$5$
140.144.5.ci.2	$140$	$2$	$2$	$5$
140.144.5.ck.1	$140$	$2$	$2$	$5$
140.144.5.ck.2	$140$	$2$	$2$	$5$
140.144.5.cy.1	$140$	$2$	$2$	$5$
140.144.5.cy.2	$140$	$2$	$2$	$5$
140.144.5.da.1	$140$	$2$	$2$	$5$
140.144.5.da.2	$140$	$2$	$2$	$5$
140.360.19.eu.1	$140$	$5$	$5$	$19$
280.144.5.qf.1	$280$	$2$	$2$	$5$
280.144.5.qf.2	$280$	$2$	$2$	$5$
280.144.5.qt.1	$280$	$2$	$2$	$5$
280.144.5.qt.2	$280$	$2$	$2$	$5$
280.144.5.ye.1	$280$	$2$	$2$	$5$
280.144.5.ye.2	$280$	$2$	$2$	$5$
280.144.5.ys.1	$280$	$2$	$2$	$5$
280.144.5.ys.2	$280$	$2$	$2$	$5$
280.144.7.hb.1	$280$	$2$	$2$	$7$
280.144.7.hc.1	$280$	$2$	$2$	$7$
280.144.7.hj.1	$280$	$2$	$2$	$7$
280.144.7.hk.1	$280$	$2$	$2$	$7$
280.144.7.hr.1	$280$	$2$	$2$	$7$
280.144.7.hr.2	$280$	$2$	$2$	$7$
280.144.7.hs.1	$280$	$2$	$2$	$7$
280.144.7.hs.2	$280$	$2$	$2$	$7$
280.144.7.hz.1	$280$	$2$	$2$	$7$
280.144.7.hz.2	$280$	$2$	$2$	$7$
280.144.7.ia.1	$280$	$2$	$2$	$7$
280.144.7.ia.2	$280$	$2$	$2$	$7$
280.144.7.id.1	$280$	$2$	$2$	$7$
280.144.7.ie.1	$280$	$2$	$2$	$7$
280.144.7.ih.1	$280$	$2$	$2$	$7$
280.144.7.ii.1	$280$	$2$	$2$	$7$