Modular curve 60.72.1.ba.1

• Label: 60.72.1.ba.1
• Level: $60$
• Index: $72$
• Genus: $1$
• Analytic rank: $0$
• Cusps: $12$
• $\Q$-cusps: $2$

Invariants

Level:	$60$		$\SL_2$-level:	$20$		Newform level:	$180$
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:	$0$
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:	20H1
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	60.72.1.36

Level structure

$\GL_2(\Z/60\Z)$-generators:	$\begin{bmatrix}11&0\\40&47\end{bmatrix}$, $\begin{bmatrix}11&15\\30&7\end{bmatrix}$, $\begin{bmatrix}21&10\\10&57\end{bmatrix}$, $\begin{bmatrix}39&35\\4&49\end{bmatrix}$, $\begin{bmatrix}59&25\\56&51\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	60.144.1-60.ba.1.1, 60.144.1-60.ba.1.2, 60.144.1-60.ba.1.3, 60.144.1-60.ba.1.4, 60.144.1-60.ba.1.5, 60.144.1-60.ba.1.6, 60.144.1-60.ba.1.7, 60.144.1-60.ba.1.8, 60.144.1-60.ba.1.9, 60.144.1-60.ba.1.10, 60.144.1-60.ba.1.11, 60.144.1-60.ba.1.12, 60.144.1-60.ba.1.13, 60.144.1-60.ba.1.14, 60.144.1-60.ba.1.15, 60.144.1-60.ba.1.16, 120.144.1-60.ba.1.1, 120.144.1-60.ba.1.2, 120.144.1-60.ba.1.3, 120.144.1-60.ba.1.4, 120.144.1-60.ba.1.5, 120.144.1-60.ba.1.6, 120.144.1-60.ba.1.7, 120.144.1-60.ba.1.8, 120.144.1-60.ba.1.9, 120.144.1-60.ba.1.10, 120.144.1-60.ba.1.11, 120.144.1-60.ba.1.12, 120.144.1-60.ba.1.13, 120.144.1-60.ba.1.14, 120.144.1-60.ba.1.15, 120.144.1-60.ba.1.16
Cyclic 60-isogeny field degree:	$8$
Cyclic 60-torsion field degree:	$128$
Full 60-torsion field degree:	$30720$

Jacobian

Conductor:	$2^{2}\cdot3^{2}\cdot5$
Simple:	yes
Squarefree:	yes
Decomposition:	$1$
Newforms:	180.2.a.a

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

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

Factor curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
5.12.0.a.2	$5$	$6$	$6$	$0$	$0$	full Jacobian
12.6.0.c.1	$12$	$12$	$12$	$0$	$0$	full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
10.36.0.a.1	$10$	$2$	$2$	$0$	$0$	full Jacobian
60.36.0.c.2	$60$	$2$	$2$	$0$	$0$	full Jacobian
60.36.1.x.1	$60$	$2$	$2$	$1$	$0$	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
60.144.5.z.2	$60$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
60.144.5.dd.2	$60$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
60.144.5.ii.2	$60$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
60.144.5.im.2	$60$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
60.144.5.kt.2	$60$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
60.144.5.kv.2	$60$	$2$	$2$	$5$	$2$	$1^{2}\cdot2$
60.144.5.kx.2	$60$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
60.144.5.ld.2	$60$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
60.216.13.cx.1	$60$	$3$	$3$	$13$	$0$	$1^{6}\cdot2^{3}$
60.288.13.jz.1	$60$	$4$	$4$	$13$	$0$	$1^{6}\cdot2^{3}$
60.360.13.t.1	$60$	$5$	$5$	$13$	$1$	$1^{6}\cdot2^{3}$
120.144.5.gw.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.vy.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.cns.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.cor.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.dee.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.des.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.dfi.2	$120$	$2$	$2$	$5$	$?$	not computed
120.144.5.dgy.2	$120$	$2$	$2$	$5$	$?$	not computed
300.360.13.m.1	$300$	$5$	$5$	$13$	$?$	not computed