Modular curve 168.72.4.jw.1

• Label: 168.72.4.jw.1
• Level: $168$
• Index: $72$
• Genus: $4$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$168$		$\SL_2$-level:	$24$		Newform level:	$1$
Index:	$72$		$\PSL_2$-index:	$72$
Genus:	$4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (none of which are rational)		Cusp widths	$6^{4}\cdot24^{2}$		Cusp orbits	$2^{3}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$3 \le \gamma \le 6$
$\overline{\Q}$-gonality:	$3 \le \gamma \le 4$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

24D4

Level structure

$\GL_2(\Z/168\Z)$-generators:	$\begin{bmatrix}17&39\\20&73\end{bmatrix}$, $\begin{bmatrix}19&160\\28&101\end{bmatrix}$, $\begin{bmatrix}49&124\\16&101\end{bmatrix}$, $\begin{bmatrix}129&49\\152&57\end{bmatrix}$, $\begin{bmatrix}153&125\\92&17\end{bmatrix}$, $\begin{bmatrix}161&139\\136&63\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	168.144.4-168.jw.1.1, 168.144.4-168.jw.1.2, 168.144.4-168.jw.1.3, 168.144.4-168.jw.1.4, 168.144.4-168.jw.1.5, 168.144.4-168.jw.1.6, 168.144.4-168.jw.1.7, 168.144.4-168.jw.1.8, 168.144.4-168.jw.1.9, 168.144.4-168.jw.1.10, 168.144.4-168.jw.1.11, 168.144.4-168.jw.1.12, 168.144.4-168.jw.1.13, 168.144.4-168.jw.1.14, 168.144.4-168.jw.1.15, 168.144.4-168.jw.1.16, 168.144.4-168.jw.1.17, 168.144.4-168.jw.1.18, 168.144.4-168.jw.1.19, 168.144.4-168.jw.1.20, 168.144.4-168.jw.1.21, 168.144.4-168.jw.1.22, 168.144.4-168.jw.1.23, 168.144.4-168.jw.1.24, 168.144.4-168.jw.1.25, 168.144.4-168.jw.1.26, 168.144.4-168.jw.1.27, 168.144.4-168.jw.1.28, 168.144.4-168.jw.1.29, 168.144.4-168.jw.1.30, 168.144.4-168.jw.1.31, 168.144.4-168.jw.1.32
Cyclic 168-isogeny field degree:	$64$
Cyclic 168-torsion field degree:	$3072$
Full 168-torsion field degree:	$2064384$

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
24.36.2.cu.1	$24$	$2$	$2$	$2$	$0$
84.36.2.s.1	$84$	$2$	$2$	$2$	$?$
168.24.0.co.1	$168$	$3$	$3$	$0$	$?$
168.36.2.cx.1	$168$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
168.144.7.dka.1	$168$	$2$	$2$	$7$
168.144.7.dkc.1	$168$	$2$	$2$	$7$
168.144.7.dkq.1	$168$	$2$	$2$	$7$
168.144.7.dks.1	$168$	$2$	$2$	$7$
168.144.7.due.1	$168$	$2$	$2$	$7$
168.144.7.dug.1	$168$	$2$	$2$	$7$
168.144.7.duy.1	$168$	$2$	$2$	$7$
168.144.7.dva.1	$168$	$2$	$2$	$7$
168.144.7.eey.1	$168$	$2$	$2$	$7$
168.144.7.efa.1	$168$	$2$	$2$	$7$
168.144.7.efo.1	$168$	$2$	$2$	$7$
168.144.7.efq.1	$168$	$2$	$2$	$7$
168.144.7.eou.1	$168$	$2$	$2$	$7$
168.144.7.eow.1	$168$	$2$	$2$	$7$
168.144.7.epk.1	$168$	$2$	$2$	$7$
168.144.7.epm.1	$168$	$2$	$2$	$7$