One refined passport of genus 9 with automorphism group $C_2\times D_{10}$

• Label: 9.40-13.0.2-2-2-10.10
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(C_2\times D_{10}\)
• Signature: \([ 0; 2, 2, 2, 10 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$C_2\times D_{10}$
Group identifier:	$[40,13]$
Signature:	$[ 0; 2, 2, 2, 10 ]$

Conjugacy classes for this refined passport:

$3, 5, 6, 16$

Jacobian variety group algebra decomposition:	$E\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s):	$3, 10, 12$

Other Data

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

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

$y^2=x^{20}+a_1x^{10}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.40-13.0.2-2-2-10.10.1

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