One refined passport of genus 14 with automorphism group $C_6$

• Label: 14.6-2.0.2-2-2-2-2-2-2-2-2-2-3-3.1
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(C_6\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$C_6$
Group identifier:	$[6,2]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3 ]$

Conjugacy classes for this refined passport:

$2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 4$

Jacobian variety group algebra decomposition:

$A_{4}\times A_{10}$

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:

$y^2=x^{30}+a_{1}x^{27}+a_{2}x^{24}+a_{3}x^{21}+a_{4}x^{18}+a_{5}x^{15}+a_{6}x^{12}+a_{7}x^{9}+a_{8}x^{6}+a_{9}x^{3}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.6-2.0.2-2-2-2-2-2-2-2-2-2-3-3.1.1

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