One refined passport of genus 10 with automorphism group $D_{22}$

• Label: 10.44-3.0.2-2-2-11.5
• Genus: \(10\)
• Quotient genus: \(0\)
• Group: \(D_{22}\)
• Signature: \([ 0; 2, 2, 2, 11 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$10$
Quotient genus:	$0$
Group name:	$D_{22}$
Group identifier:	$[44,3]$
Signature:	$[ 0; 2, 2, 2, 11 ]$

Conjugacy classes for this refined passport:

$2, 3, 4, 9$

Jacobian variety group algebra decomposition:	$A_{5}^{2}$
Corresponding character(s):	$6$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22) (23,34) (24,35) (25,36) (26,37) (27,38) (28,39) (29,40) (30,41) (31,42) (32,43) (33,44)
Cyclic trigonal curve(s):	no

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

$y^2=x^{22}+a_1x^{11}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

10.44-3.0.2-2-2-11.5.1

	(1,12) (2,13) (3,14) (4,15) (5,16) (6,17) (7,18) (8,19) (9,20) (10,21) (11,22) (23,34) (24,35) (25,36) (26,37) (27,38) (28,39) (29,40) (30,41) (31,42) (32,43) (33,44)
	(1,23) (2,33) (3,32) (4,31) (5,30) (6,29) (7,28) (8,27) (9,26) (10,25) (11,24) (12,34) (13,44) (14,43) (15,42) (16,41) (17,40) (18,39) (19,38) (20,37) (21,36) (22,35)
	(1,40) (2,39) (3,38) (4,37) (5,36) (6,35) (7,34) (8,44) (9,43) (10,42) (11,41) (12,29) (13,28) (14,27) (15,26) (16,25) (17,24) (18,23) (19,33) (20,32) (21,31) (22,30)
	(1,6,11,5,10,4,9,3,8,2,7) (12,17,22,16,21,15,20,14,19,13,18) (23,28,33,27,32,26,31,25,30,24,29) (34,39,44,38,43,37,42,36,41,35,40)