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

• Label: 9.80-14.0.2-4-20.2
• 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:

$5, 9, 21$

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.

9.80-14.0.2-4-20.2.1

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