One refined passport of genus 6 with automorphism group $\GL(2,3)$

• Label: 6.48-29.0.2-6-8.1
• Genus: \(6\)
• Quotient genus: \(0\)
• Group: \(\GL(2,3)\)
• Signature: \([ 0; 2, 6, 8 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$6$
Quotient genus:	$0$
Group name:	$\GL(2,3)$
Group identifier:	$[48,29]$
Signature:	$[ 0; 2, 6, 8 ]$

Conjugacy classes for this refined passport:

$3, 6, 7$

Jacobian variety group algebra decomposition:	$E^{2}\times E^{4}$
Corresponding character(s):	$4, 8$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,2) (3,4) (5,6) (7,8) (9,10) (11,12) (13,14) (15,16) (17,18) (19,20) (21,22) (23,24) (25,26) (27,28) (29,30) (31,32) (33,34) (35,36) (37,38) (39,40) (41,42) (43,44) (45,46) (47,48)
Cyclic trigonal curve(s):	no

Equation(s) of curve(s) in this refined passport:

$y^2=x(x^4-1)(x^8+14x^4+1)$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

6.48-29.0.2-6-8.1.1

	(1,25) (2,26) (3,29) (4,30) (5,27) (6,28) (7,32) (8,31) (9,41) (10,42) (11,45) (12,46) (13,43) (14,44) (15,48) (16,47) (17,33) (18,34) (19,37) (20,38) (21,35) (22,36) (23,40) (24,39)
	(1,15,19,2,16,20) (3,10,24,4,9,23) (5,14,21,6,13,22) (7,11,18,8,12,17) (25,39,43,26,40,44) (27,34,48,28,33,47) (29,38,45,30,37,46) (31,35,42,32,36,41)
	(1,38,3,40,2,37,4,39) (5,36,7,33,6,35,8,34) (9,30,11,32,10,29,12,31) (13,28,15,25,14,27,16,26) (17,46,19,48,18,45,20,47) (21,44,23,41,22,43,24,42)