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

• Label: 10.44-3.0.2-2-2-11.3
• 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:

$2, 3, 4, 7$

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.

10.44-3.0.2-2-2-11.3.1

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