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

• Label: 9.120-35.0.2-5-6.2
• 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:

$3, 7, 8$

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.

9.120-35.0.2-5-6.2.1

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