One refined passport of genus 3 with automorphism group $\SL(2,3):C_2$

• Label: 3.48-33.0.2-3-12.1
• Genus: \(3\)
• Quotient genus: \(0\)
• Group: \(\SL(2,3):C_2\)
• Signature: \([ 0; 2, 3, 12 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$3$
Quotient genus:	$0$
Group name:	$\SL(2,3):C_2$
Group identifier:	$[48,33]$
Signature:	$[ 0; 2, 3, 12 ]$

Conjugacy classes for this refined passport:

$3, 4, 12$

Jacobian variety group algebra decomposition:	$E\times E^{2}$
Corresponding character(s):	$3, 7$

Other Data

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

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

$y^4 = x^3-1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

3.48-33.0.2-3-12.1.1

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