One refined passport of genus 10 with automorphism group $D_{20}$

• Label: 10.40-6.0.2-2-2-20.3
• Genus: \(10\)
• Quotient genus: \(0\)
• Group: \(D_{20}\)
• Signature: \([ 0; 2, 2, 2, 20 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$D_{20}$
Group identifier:	$[40,6]$
Signature:	$[ 0; 2, 2, 2, 20 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 12$

Jacobian variety group algebra decomposition:	$E^{2}\times A_{4}^{2}$
Corresponding character(s):	$5, 10$

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:

$y^2=x(x^{20}+a_{1}x^{10}+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.40-6.0.2-2-2-20.3.1

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