One refined passport of genus 4 with automorphism group $C_5:D_4$

• Label: 4.40-8.0.2-4-10.1
• Genus: \(4\)
• Quotient genus: \(0\)
• Group: \(C_5:D_4\)
• Signature: \([ 0; 2, 4, 10 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$4$
Quotient genus:	$0$
Group name:	$C_5:D_4$
Group identifier:	$[40,8]$
Signature:	$[ 0; 2, 4, 10 ]$

Conjugacy classes for this refined passport:

$4, 5, 10$

Jacobian variety group algebra decomposition:	$A_{2}^{2}$
Corresponding character(s):	$9$

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:

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

Generating vector(s)

Displaying the unique generating vector for this refined passport.

4.40-8.0.2-4-10.1.1

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