One refined passport of genus 15 with automorphism group $D_{16}:C_4$

• Label: 15.128-147.0.2-4-32.2
• Genus: \(15\)
• Quotient genus: \(0\)
• Group: \(D_{16}:C_4\)
• Signature: \([ 0; 2, 4, 32 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$15$
Quotient genus:	$0$
Group name:	$D_{16}:C_4$
Group identifier:	$[128,147]$
Signature:	$[ 0; 2, 4, 32 ]$

Conjugacy classes for this refined passport:

$5, 9, 26$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$6, 13, 16, 23$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,9) (2,10) (3,11) (4,12) (5,13) (6,14) (7,15) (8,16) (17,25) (18,26) (19,27) (20,28) (21,29) (22,30) (23,31) (24,32) (33,41) (34,42) (35,43) (36,44) (37,45) (38,46) (39,47) (40,48) (49,57) (50,58) (51,59) (52,60) (53,61) (54,62) (55,63) (56,64) (65,73) (66,74) (67,75) (68,76) (69,77) (70,78) (71,79) (72,80) (81,89) (82,90) (83,91) (84,92) (85,93) (86,94) (87,95) (88,96) (97,105) (98,106) (99,107) (100,108) (101,109) (102,110) (103,111) (104,112) (113,121) (114,122) (115,123) (116,124) (117,125) (118,126) (119,127) (120,128)
Cyclic trigonal curve(s):	no

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

$y^2=x^{32}-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

15.128-147.0.2-4-32.2.1

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