One refined passport of genus 5 with automorphism group $C_4\times D_5$

• Label: 5.40-5.0.2-4-20.1
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_4\times D_5\)
• Signature: \([ 0; 2, 4, 20 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$5$
Quotient genus:	$0$
Group name:	$C_4\times D_5$
Group identifier:	$[40,5]$
Signature:	$[ 0; 2, 4, 20 ]$

Conjugacy classes for this refined passport:

$3, 7, 14$

Jacobian variety group algebra decomposition:	$E\times A_{2}^{2}$
Corresponding character(s):	$6, 13$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,6) (2,7) (3,8) (4,9) (5,10) (11,16) (12,17) (13,18) (14,19) (15,20) (21,26) (22,27) (23,28) (24,29) (25,30) (31,36) (32,37) (33,38) (34,39) (35,40)
Cyclic trigonal curve(s):	no

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

$y^2=x(x^{10}-1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

5.40-5.0.2-4-20.1.1

	(1,21) (2,25) (3,24) (4,23) (5,22) (6,26) (7,30) (8,29) (9,28) (10,27) (11,31) (12,35) (13,34) (14,33) (15,32) (16,36) (17,40) (18,39) (19,38) (20,37)
	(1,33,6,38) (2,32,7,37) (3,31,8,36) (4,35,9,40) (5,34,10,39) (11,28,16,23) (12,27,17,22) (13,26,18,21) (14,30,19,25) (15,29,20,24)
	(1,19,7,15,3,16,9,12,5,18,6,14,2,20,8,11,4,17,10,13) (21,39,27,35,23,36,29,32,25,38,26,34,22,40,28,31,24,37,30,33)