One refined passport of genus 13 with automorphism group $C_4$

• Label: 13.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.2
• Genus: \(13\)
• Quotient genus: \(0\)
• Group: \(C_4\)
• Signature: \([ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$13$
Quotient genus:	$0$
Group name:	$C_4$
Group identifier:	$[4,1]$
Signature:	$[ 0; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ]$

Conjugacy classes for this refined passport:

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

Jacobian variety group algebra decomposition:

$A_{13}$

Other Data

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

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

$y^2=x(x^{26}+a_{1}x^{24}+a_{2}x^{22}+a_{3}x^{20}+a_{4}x^{18}+a_{5}x^{16}+a_{6}x^{14}+a_{7}x^{12}+a_{8}x^{10}+a_{9}x^{8}+a_{10}x^{6}+a_{11}x^{4}+a_{12}x^{2}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

13.4-1.0.2-2-2-2-2-2-2-2-2-2-2-2-2-4-4.2.1

	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,2) (3,4)
	(1,4,2,3)
	(1,4,2,3)