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

• Label: 15.128-147.0.2-4-32.12
• 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:

$5, 10, 29$

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.

15.128-147.0.2-4-32.12.1

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