Modular curve 140.72.1.t.2

• Label: 140.72.1.t.2
• Level: $140$
• Index: $72$
• Genus: $1$
• Cusps: $12$
• $\Q$-cusps: $2$

Invariants

Level:	$140$		$\SL_2$-level:	$20$		Newform level:	$1$
Index:	$72$		$\PSL_2$-index:	$72$
Genus:	$1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps:	$12$ (of which $2$ are rational)		Cusp widths	$1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$		Cusp orbits	$1^{2}\cdot2^{3}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

20H1

Level structure

$\GL_2(\Z/140\Z)$-generators:	$\begin{bmatrix}23&48\\120&11\end{bmatrix}$, $\begin{bmatrix}27&72\\116&103\end{bmatrix}$, $\begin{bmatrix}41&38\\32&97\end{bmatrix}$, $\begin{bmatrix}60&31\\111&0\end{bmatrix}$, $\begin{bmatrix}110&1\\63&58\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	140.144.1-140.t.2.1, 140.144.1-140.t.2.2, 140.144.1-140.t.2.3, 140.144.1-140.t.2.4, 140.144.1-140.t.2.5, 140.144.1-140.t.2.6, 140.144.1-140.t.2.7, 140.144.1-140.t.2.8, 140.144.1-140.t.2.9, 140.144.1-140.t.2.10, 140.144.1-140.t.2.11, 140.144.1-140.t.2.12, 140.144.1-140.t.2.13, 140.144.1-140.t.2.14, 140.144.1-140.t.2.15, 140.144.1-140.t.2.16, 280.144.1-140.t.2.1, 280.144.1-140.t.2.2, 280.144.1-140.t.2.3, 280.144.1-140.t.2.4, 280.144.1-140.t.2.5, 280.144.1-140.t.2.6, 280.144.1-140.t.2.7, 280.144.1-140.t.2.8, 280.144.1-140.t.2.9, 280.144.1-140.t.2.10, 280.144.1-140.t.2.11, 280.144.1-140.t.2.12, 280.144.1-140.t.2.13, 280.144.1-140.t.2.14, 280.144.1-140.t.2.15, 280.144.1-140.t.2.16
Cyclic 140-isogeny field degree:	$16$
Cyclic 140-torsion field degree:	$384$
Full 140-torsion field degree:	$1290240$

Jacobian

Conductor:	$?$
Simple:	yes
Squarefree:	yes
Decomposition:	$1$
Newforms:	not computed

Rational points

This modular curve is an elliptic curve, but the rank has not been computed

Modular covers

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

Factor curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_{\pm1}(5)$	$5$	$6$	$6$	$0$	$0$	full Jacobian
28.6.0.b.1	$28$	$12$	$12$	$0$	$0$	full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_{\pm1}(10)$	$10$	$2$	$2$	$0$	$0$	full Jacobian
140.36.0.c.1	$140$	$2$	$2$	$0$	$?$	full Jacobian
140.36.1.b.1	$140$	$2$	$2$	$1$	$?$	dimension zero

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

Covering curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
140.144.5.a.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.bc.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.dk.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.ds.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.gm.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.gq.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.gv.1	$140$	$2$	$2$	$5$	$?$	not computed
140.144.5.gy.1	$140$	$2$	$2$	$5$	$?$	not computed
140.360.13.y.1	$140$	$5$	$5$	$13$	$?$	not computed
280.144.5.dk.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.hr.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.bbw.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.bdr.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.bwy.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.bya.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.bzk.1	$280$	$2$	$2$	$5$	$?$	not computed
280.144.5.caf.1	$280$	$2$	$2$	$5$	$?$	not computed