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

• Label: 12.84-8.0.2-6-14.2
• 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:

$4, 6, 11$

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.

12.84-8.0.2-6-14.2.1

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