One refined passport of genus 5 with automorphism group $C_2^3$

• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2^3\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2 ]\)
• Generating Vectors: \(1\)

Family Information

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

Conjugacy classes for this refined passport:

2, 4, 4, 4, 6, 8

Jacobian variety group algebra decomposition:	$E\times E\times E\times A_{2}$
Corresponding character(s):	3, 4, 7, 8

Other Data

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

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

$y^2=(x^{4}+a_{1}x^{2}+1)(x^{4}+a_{2}x^{2}+1)(x^{4}+a_{3}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.8-5.0.2-2-2-2-2-2.35.1

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