One refined passport of genus 3 with automorphism group $C_2\times C_4$

• Label: 3.8-2.0.2-2-4-4.9
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(C_2\times C_4\)
• Signature: \([ 0; 2, 2, 4, 4 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$3$
Quotient genus:	$0$
Group name:	$C_2\times C_4$
Group identifier:	$[8,2]$
Signature:	$[ 0; 2, 2, 4, 4 ]$

Conjugacy classes for this refined passport:

$3, 4, 7, 7$

The full automorphism group for this family is $D_4:C_2$ with signature $[ 0; 2, 2, 2, 4 ]$.

Jacobian variety group algebra decomposition:	$E\times E\times E$
Corresponding character(s):	$3, 4, 6$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

3.8-2.0.2-2-4-4.9.1

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