Modular curve 140.72.3.cu.2

• Label: 140.72.3.cu.2
• 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:

20G3

Level structure

$\GL_2(\Z/140\Z)$-generators:	$\begin{bmatrix}26&35\\59&102\end{bmatrix}$, $\begin{bmatrix}34&57\\21&40\end{bmatrix}$, $\begin{bmatrix}37&44\\124&77\end{bmatrix}$, $\begin{bmatrix}39&50\\2&77\end{bmatrix}$, $\begin{bmatrix}135&116\\16&45\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	140.144.3-140.cu.2.1, 140.144.3-140.cu.2.2, 140.144.3-140.cu.2.3, 140.144.3-140.cu.2.4, 140.144.3-140.cu.2.5, 140.144.3-140.cu.2.6, 140.144.3-140.cu.2.7, 140.144.3-140.cu.2.8, 140.144.3-140.cu.2.9, 140.144.3-140.cu.2.10, 140.144.3-140.cu.2.11, 140.144.3-140.cu.2.12, 140.144.3-140.cu.2.13, 140.144.3-140.cu.2.14, 140.144.3-140.cu.2.15, 140.144.3-140.cu.2.16, 280.144.3-140.cu.2.1, 280.144.3-140.cu.2.2, 280.144.3-140.cu.2.3, 280.144.3-140.cu.2.4, 280.144.3-140.cu.2.5, 280.144.3-140.cu.2.6, 280.144.3-140.cu.2.7, 280.144.3-140.cu.2.8, 280.144.3-140.cu.2.9, 280.144.3-140.cu.2.10, 280.144.3-140.cu.2.11, 280.144.3-140.cu.2.12, 280.144.3-140.cu.2.13, 280.144.3-140.cu.2.14, 280.144.3-140.cu.2.15, 280.144.3-140.cu.2.16
Cyclic 140-isogeny field degree:	$16$
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
$X_{\pm1}(5)$	$5$	$6$	$6$	$0$	$0$
28.6.0.d.1	$28$	$12$	$12$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
$X_{\pm1}(10)$	$10$	$2$	$2$	$0$	$0$
140.36.1.i.1	$140$	$2$	$2$	$1$	$?$
140.36.2.b.2	$140$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
140.144.5.b.1	$140$	$2$	$2$	$5$
140.144.5.bc.1	$140$	$2$	$2$	$5$
140.144.5.cf.1	$140$	$2$	$2$	$5$
140.144.5.ci.1	$140$	$2$	$2$	$5$
140.144.5.eq.1	$140$	$2$	$2$	$5$
140.144.5.ey.1	$140$	$2$	$2$	$5$
140.144.5.fg.1	$140$	$2$	$2$	$5$
140.144.5.fk.1	$140$	$2$	$2$	$5$
140.360.19.jo.1	$140$	$5$	$5$	$19$
280.144.5.ei.1	$280$	$2$	$2$	$5$
280.144.5.hs.1	$280$	$2$	$2$	$5$
280.144.5.pn.1	$280$	$2$	$2$	$5$
280.144.5.qi.1	$280$	$2$	$2$	$5$
280.144.5.bkq.1	$280$	$2$	$2$	$5$
280.144.5.bmi.1	$280$	$2$	$2$	$5$
280.144.5.bom.1	$280$	$2$	$2$	$5$
280.144.5.bpo.1	$280$	$2$	$2$	$5$