Modular curve 120.24.1.iw.1

• Label: 120.24.1.iw.1
• Level: $120$
• Index: $24$
• Genus: $1$
• Cusps: $4$
• $\Q$-cusps: $4$

Invariants

Level:	$120$		$\SL_2$-level:	$12$		Newform level:	$1$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps:	$4$ (all of which are rational)		Cusp widths	$2\cdot4\cdot6\cdot12$		Cusp orbits	$1^{4}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

12F1

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}3&112\\46&57\end{bmatrix}$, $\begin{bmatrix}9&86\\80&99\end{bmatrix}$, $\begin{bmatrix}45&34\\32&43\end{bmatrix}$, $\begin{bmatrix}70&21\\79&104\end{bmatrix}$, $\begin{bmatrix}74&3\\99&110\end{bmatrix}$, $\begin{bmatrix}109&72\\10&77\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.48.1-120.iw.1.1, 120.48.1-120.iw.1.2, 120.48.1-120.iw.1.3, 120.48.1-120.iw.1.4, 120.48.1-120.iw.1.5, 120.48.1-120.iw.1.6, 120.48.1-120.iw.1.7, 120.48.1-120.iw.1.8, 120.48.1-120.iw.1.9, 120.48.1-120.iw.1.10, 120.48.1-120.iw.1.11, 120.48.1-120.iw.1.12, 120.48.1-120.iw.1.13, 120.48.1-120.iw.1.14, 120.48.1-120.iw.1.15, 120.48.1-120.iw.1.16, 120.48.1-120.iw.1.17, 120.48.1-120.iw.1.18, 120.48.1-120.iw.1.19, 120.48.1-120.iw.1.20, 120.48.1-120.iw.1.21, 120.48.1-120.iw.1.22, 120.48.1-120.iw.1.23, 120.48.1-120.iw.1.24, 120.48.1-120.iw.1.25, 120.48.1-120.iw.1.26, 120.48.1-120.iw.1.27, 120.48.1-120.iw.1.28, 120.48.1-120.iw.1.29, 120.48.1-120.iw.1.30, 120.48.1-120.iw.1.31, 120.48.1-120.iw.1.32
Cyclic 120-isogeny field degree:	$24$
Cyclic 120-torsion field degree:	$768$
Full 120-torsion field degree:	$1474560$

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
$X_0(3)$	$3$	$6$	$6$	$0$	$0$	full Jacobian
40.6.0.e.1	$40$	$4$	$4$	$0$	$0$	full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_0(6)$	$6$	$2$	$2$	$0$	$0$	full Jacobian
40.6.0.e.1	$40$	$4$	$4$	$0$	$0$	full Jacobian

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

Covering curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
120.48.1.dh.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.gg.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.jw.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.jx.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.yz.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.za.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.zc.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.zd.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.bkw.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.bkx.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.blc.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.bld.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.bli.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.blj.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.blo.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.48.1.blp.1	$120$	$2$	$2$	$1$	$?$	dimension zero
120.72.3.dnu.1	$120$	$3$	$3$	$3$	$?$	not computed
120.120.9.xi.1	$120$	$5$	$5$	$9$	$?$	not computed
120.144.9.rvc.1	$120$	$6$	$6$	$9$	$?$	not computed
120.240.17.gie.1	$120$	$10$	$10$	$17$	$?$	not computed