One refined passport of genus 9 with automorphism group $C_2\times A_5$

• Label: 9.120-35.0.2-5-6.1
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(C_2\times A_5\)
• Signature: \([ 0; 2, 5, 6 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$C_2\times A_5$
Group identifier:	$[120,35]$
Signature:	$[ 0; 2, 5, 6 ]$

Conjugacy classes for this refined passport:

$3, 6, 8$

Jacobian variety group algebra decomposition:	$E^{4}\times E^{5}$
Corresponding character(s):	$8, 10$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,61) (2,62) (3,63) (4,64) (5,65) (6,66) (7,67) (8,68) (9,69) (10,70) (11,71) (12,72) (13,73) (14,74) (15,75) (16,76) (17,77) (18,78) (19,79) (20,80) (21,81) (22,82) (23,83) (24,84) (25,85) (26,86) (27,87) (28,88) (29,89) (30,90) (31,91) (32,92) (33,93) (34,94) (35,95) (36,96) (37,97) (38,98) (39,99) (40,100) (41,101) (42,102) (43,103) (44,104) (45,105) (46,106) (47,107) (48,108) (49,109) (50,110) (51,111) (52,112) (53,113) (54,114) (55,115) (56,116) (57,117) (58,118) (59,119) (60,120)
Cyclic trigonal curve(s):	no

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

$y^2=x^{20}-228x^{15}+494x^{10}+228x^5+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.120-35.0.2-5-6.1.1

	(1,6) (2,5) (3,14) (4,38) (7,10) (8,29) (9,108) (11,16) (12,15) (13,99) (17,20) (18,104) (19,53) (21,26) (22,25) (23,34) (24,58) (27,30) (28,49) (31,36) (32,35) (33,119) (37,40) (39,73) (41,46) (42,45) (43,54) (44,78) (47,50) (48,69) (51,56) (52,55) (57,60) (59,93) (61,66) (62,65) (63,74) (64,98) (67,70) (68,89) (71,76) (72,75) (77,80) (79,113) (81,86) (82,85) (83,94) (84,118) (87,90) (88,109) (91,96) (92,95) (97,100) (101,106) (102,105) (103,114) (107,110) (111,116) (112,115) (117,120)
	(1,27,65,68,44) (2,95,98,19,31) (3,34,66,72,10) (4,81,107,25,28) (5,8,104,61,87) (6,12,70,63,94) (7,45,48,24,101) (9,76,37,20,13) (11,102,75,78,119) (14,46,52,110,103) (15,18,59,71,42) (16,97,80,73,69) (17,120,113,109,56) (21,47,85,88,64) (22,115,118,39,51) (23,54,86,92,30) (26,32,90,83,114) (29,96,57,40,33) (35,38,79,91,62) (36,117,100,93,89) (41,67,105,108,84) (43,74,106,112,50) (49,116,77,60,53) (55,58,99,111,82)
	(1,78,72,61,18,12) (2,36,68,62,96,8) (3,7,106,63,67,46) (4,49,19,64,109,79) (5,90,35,65,30,95) (6,83,87,66,23,27) (9,99,24,69,39,84) (10,75,105,70,15,45) (11,33,37,71,93,97) (13,17,51,73,77,111) (14,114,94,74,54,34) (16,48,42,76,108,102) (20,40,60,80,100,120) (21,98,92,81,38,32) (22,56,88,82,116,28) (25,110,55,85,50,115) (26,103,107,86,43,47) (29,119,44,89,59,104) (31,53,57,91,113,117) (41,118,112,101,58,52)