One refined passport of genus 4 with automorphism group $C_{18}$

• Label: 4.18-2.0.2-9-18.6
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_{18}\)
• Signature: \([ 0; 2, 9, 18 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$4$
Quotient genus:	$0$
Group name:	$C_{18}$
Group identifier:	$[18,2]$
Signature:	$[ 0; 2, 9, 18 ]$

Conjugacy classes for this refined passport:

$2, 12, 13$

Jacobian variety group algebra decomposition:

$A_{3}\times E$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x^{9}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

4.18-2.0.2-9-18.6.1

	(1,10) (2,11) (3,12) (4,13) (5,14) (6,15) (7,16) (8,17) (9,18)
	(1,9,6,3,8,5,2,7,4) (10,18,15,12,17,14,11,16,13)
	(1,13,7,11,5,17,3,15,9,10,4,16,2,14,8,12,6,18)