Family of genus 5 curves with automorphism group $C_2^4:D_5$

• Label: 5.160-234.0.2-4-5
• Genus: \(5\)
• Quotient genus: \(0\)
• Group: \(C_2^4:D_5\)
• Signature: \([ 0; 2, 4, 5 ]\)

Family Information

Genus:	$5$
Dimension of the family:	$0$

Cover

Quotient genus:	$0$
Number of branch points:	$3$
Signature:	$[ 0; 2, 4, 5 ]$

Group

Name:	$C_2^4:D_5$
Identifier:	$[160,234]$

Conjugacy class(es) of Refined passports

Refined passport label	Conjugacy classes
5.160-234.0.2-4-5.1	5, 6, 9
5.160-234.0.2-4-5.2	5, 6, 10
5.160-234.0.2-4-5.3	5, 7, 9
5.160-234.0.2-4-5.4	5, 7, 10
5.160-234.0.2-4-5.5	5, 8, 9
5.160-234.0.2-4-5.6	5, 8, 10

Displaying the representative for the unique action up to topological equivalence.

5.160-234.0.2-4-5.1.1

	(1,81) (2,91) (3,94) (4,88) (5,85) (6,95) (7,90) (8,84) (9,93) (10,87) (11,82) (12,92) (13,89) (14,83) (15,86) (16,96) (17,145) (18,155) (19,158) (20,152) (21,149) (22,159) (23,154) (24,148) (25,157) (26,151) (27,146) (28,156) (29,153) (30,147) (31,150) (32,160) (33,129) (34,139) (35,142) (36,136) (37,133) (38,143) (39,138) (40,132) (41,141) (42,135) (43,130) (44,140) (45,137) (46,131) (47,134) (48,144) (49,113) (50,123) (51,126) (52,120) (53,117) (54,127) (55,122) (56,116) (57,125) (58,119) (59,114) (60,124) (61,121) (62,115) (63,118) (64,128) (65,97) (66,107) (67,110) (68,104) (69,101) (70,111) (71,106) (72,100) (73,109) (74,103) (75,98) (76,108) (77,105) (78,99) (79,102) (80,112)
	(1,157,14,146) (2,145,13,158) (3,156,16,151) (4,152,15,155) (5,150,10,153) (6,154,9,149) (7,147,12,160) (8,159,11,148) (17,141,30,130) (18,129,29,142) (19,140,32,135) (20,136,31,139) (21,134,26,137) (22,138,25,133) (23,131,28,144) (24,143,27,132) (33,125,46,114) (34,113,45,126) (35,124,48,119) (36,120,47,123) (37,118,42,121) (38,122,41,117) (39,115,44,128) (40,127,43,116) (49,109,62,98) (50,97,61,110) (51,108,64,103) (52,104,63,107) (53,102,58,105) (54,106,57,101) (55,99,60,112) (56,111,59,100) (65,93,78,82) (66,81,77,94) (67,92,80,87) (68,88,79,91) (69,86,74,89) (70,90,73,85) (71,83,76,96) (72,95,75,84)
	(1,27,38,53,77) (2,19,42,63,68) (3,26,47,52,66) (4,18,35,58,79) (5,29,33,59,70) (6,21,45,49,75) (7,32,44,62,73) (8,24,40,56,72) (9,23,48,60,78) (10,31,36,50,67) (11,22,37,61,65) (12,30,41,55,80) (13,17,43,54,69) (14,25,39,64,76) (15,20,34,51,74) (16,28,46,57,71) (81,107,118,133,157) (82,99,122,143,148) (83,106,127,132,146) (84,98,115,138,159) (85,109,113,139,150) (86,101,125,129,155) (87,112,124,142,153) (88,104,120,136,152) (89,103,128,140,158) (90,111,116,130,147) (91,102,117,141,145) (92,110,121,135,160) (93,97,123,134,149) (94,105,119,144,156) (95,100,114,131,154) (96,108,126,137,151)