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

• Label: 15.128-147.0.2-4-32.28
• 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:

$6, 10, 30$

Jacobian variety group algebra decomposition:	$E\times E^{2}\times A_{2}^{2}\times A_{4}^{2}$
Corresponding character(s):	$5, 13, 16, 23$

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.

15.128-147.0.2-4-32.28.1

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