One refined passport of genus 14 with automorphism group $D_4$

• Label: 14.8-3.0.2-2-2-2-2-2-2-2-2-4.1
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(D_4\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 4 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$D_4$
Group identifier:	$[8,3]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 4 ]$

Conjugacy classes for this refined passport:

$2, 2, 2, 2, 2, 2, 2, 3, 4, 5$

Jacobian variety group algebra decomposition:	$A_{7}^{2}$
Corresponding character(s):	$5$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,2) (3,4) (5,6) (7,8)
Cyclic trigonal curve(s):	no

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

	$y^2=x(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)(x^{4}+a_{6}x^{2}+1)(x^{4}+a_{7}x^{2}+1)$
	$y^2=(x^{2}-1)(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)(x^{4}+a_{6}x^{2}+1)(x^{4}+a_{7}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.8-3.0.2-2-2-2-2-2-2-2-2-4.1.1

	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,2) (3,4) (5,6) (7,8)
	(1,3) (2,4) (5,7) (6,8)
	(1,5) (2,6) (3,8) (4,7)
	(1,8,2,7) (3,5,4,6)