One refined passport of genus 12 with automorphism group $C_6$

• Label: 12.6-2.0.2-2-2-2-2-2-2-2-6-6.1
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_6\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 6, 6 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_6$
Group identifier:	$[6,2]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 6, 6 ]$

Conjugacy classes for this refined passport:

$2, 2, 2, 2, 2, 2, 2, 2, 5, 6$

Jacobian variety group algebra decomposition:

$A_{4}\times A_{8}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,4) (2,5) (3,6)
Cyclic trigonal curve(s):	no

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

$y^2=x(x^{24}+a_{1}x^{21}+a_{2}x^{18}+a_{3}x^{15}+a_{4}x^{12}+a_{5}x^{9}+a_{6}x^{6}+a_{7}x^{3}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.6-2.0.2-2-2-2-2-2-2-2-6-6.1.1

	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,4) (2,5) (3,6)
	(1,5,3,4,2,6)
	(1,6,2,4,3,5)