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

• Label: 5.40-5.0.2-4-20.3
• 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:

$3, 8, 13$

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.

5.40-5.0.2-4-20.3.1

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