One refined passport of genus 12 with automorphism group $S_3\times D_7$

• Label: 12.84-8.0.2-6-14.1
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(S_3\times D_7\)
• Signature: \([ 0; 2, 6, 14 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$S_3\times D_7$
Group identifier:	$[84,8]$
Signature:	$[ 0; 2, 6, 14 ]$

Conjugacy classes for this refined passport:

$4, 6, 10$

Jacobian variety group algebra decomposition:	$A_{3}^{4}$
Corresponding character(s):	$13$

Other Data

Hyperelliptic curve(s):	no
Cyclic trigonal curve(s):	yes
Trigonal automorphism:	(1,8,15) (2,9,16) (3,10,17) (4,11,18) (5,12,19) (6,13,20) (7,14,21) (22,29,36) (23,30,37) (24,31,38) (25,32,39) (26,33,40) (27,34,41) (28,35,42) (43,50,57) (44,51,58) (45,52,59) (46,53,60) (47,54,61) (48,55,62) (49,56,63) (64,71,78) (65,72,79) (66,73,80) (67,74,81) (68,75,82) (69,76,83) (70,77,84)

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.84-8.0.2-6-14.1.1

	(1,64) (2,70) (3,69) (4,68) (5,67) (6,66) (7,65) (8,78) (9,84) (10,83) (11,82) (12,81) (13,80) (14,79) (15,71) (16,77) (17,76) (18,75) (19,74) (20,73) (21,72) (22,43) (23,49) (24,48) (25,47) (26,46) (27,45) (28,44) (29,57) (30,63) (31,62) (32,61) (33,60) (34,59) (35,58) (36,50) (37,56) (38,55) (39,54) (40,53) (41,52) (42,51)
	(1,56,15,49,8,63) (2,55,16,48,9,62) (3,54,17,47,10,61) (4,53,18,46,11,60) (5,52,19,45,12,59) (6,51,20,44,13,58) (7,50,21,43,14,57) (22,77,36,70,29,84) (23,76,37,69,30,83) (24,75,38,68,31,82) (25,74,39,67,32,81) (26,73,40,66,33,80) (27,72,41,65,34,79) (28,71,42,64,35,78)
	(1,30,3,32,5,34,7,29,2,31,4,33,6,35) (8,23,10,25,12,27,14,22,9,24,11,26,13,28) (15,37,17,39,19,41,21,36,16,38,18,40,20,42) (43,72,45,74,47,76,49,71,44,73,46,75,48,77) (50,65,52,67,54,69,56,64,51,66,53,68,55,70) (57,79,59,81,61,83,63,78,58,80,60,82,62,84)