One refined passport of genus 15 with automorphism group $C_2^3$

• Label: 15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.819
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(C_2^3\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$C_2^3$
Group identifier:	$[8,5]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 8, 8, 8, 8, 8, 8, 8, 8$

Jacobian variety group algebra decomposition:	$A_{4}\times A_{4}\times A_{3}\times A_{4}$
Corresponding character(s):	$2, 3, 5, 8$

Other Data

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

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

$y^2=(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)(x^{4}+a_{4}x^{2}+1)(x^{4}+a_{5}x^{2}+1)(x^{4}+a_{6}x^{2}+1)(x^{4}+a_{7}x^{2}+1)(x^{4}+a_{8}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.8-5.0.2-2-2-2-2-2-2-2-2-2-2.819.1

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