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

• Label: 15.128-147.0.2-4-32.3
• 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:

$5, 9, 28$

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.

15.128-147.0.2-4-32.3.1

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