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

• Label: 4.18-2.0.2-9-18.3
• 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:

$2, 9, 14$

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.

4.18-2.0.2-9-18.3.1

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