One refined passport of genus 9 with automorphism group $D_{10}:C_4$

• Label: 9.80-14.0.2-4-20.10
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(D_{10}:C_4\)
• Signature: \([ 0; 2, 4, 20 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$D_{10}:C_4$
Group identifier:	$[80,14]$
Signature:	$[ 0; 2, 4, 20 ]$

Conjugacy classes for this refined passport:

$6, 9, 22$

Jacobian variety group algebra decomposition:	$E\times A_{2}^{2}\times A_{2}^{2}$
Corresponding character(s):	$6, 12, 19$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,16) (2,17) (3,18) (4,19) (5,20) (6,11) (7,12) (8,13) (9,14) (10,15) (21,36) (22,37) (23,38) (24,39) (25,40) (26,31) (27,32) (28,33) (29,34) (30,35) (41,56) (42,57) (43,58) (44,59) (45,60) (46,51) (47,52) (48,53) (49,54) (50,55) (61,76) (62,77) (63,78) (64,79) (65,80) (66,71) (67,72) (68,73) (69,74) (70,75)
Cyclic trigonal curve(s):	no

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

$y^2=x^{20}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.80-14.0.2-4-20.10.1

	(1,51) (2,55) (3,54) (4,53) (5,52) (6,56) (7,60) (8,59) (9,58) (10,57) (11,41) (12,45) (13,44) (14,43) (15,42) (16,46) (17,50) (18,49) (19,48) (20,47) (21,76) (22,80) (23,79) (24,78) (25,77) (26,71) (27,75) (28,74) (29,73) (30,72) (31,66) (32,70) (33,69) (34,68) (35,67) (36,61) (37,65) (38,64) (39,63) (40,62)
	(1,62,16,77) (2,61,17,76) (3,65,18,80) (4,64,19,79) (5,63,20,78) (6,67,11,72) (7,66,12,71) (8,70,13,75) (9,69,14,74) (10,68,15,73) (21,57,36,42) (22,56,37,41) (23,60,38,45) (24,59,39,44) (25,58,40,43) (26,52,31,47) (27,51,32,46) (28,55,33,50) (29,54,34,49) (30,53,35,48)
	(1,25,14,33,2,21,15,34,3,22,11,35,4,23,12,31,5,24,13,32) (6,30,19,38,7,26,20,39,8,27,16,40,9,28,17,36,10,29,18,37) (41,65,54,73,42,61,55,74,43,62,51,75,44,63,52,71,45,64,53,72) (46,70,59,78,47,66,60,79,48,67,56,80,49,68,57,76,50,69,58,77)