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

• Label: 3.48-33.0.2-3-12.4
• 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:

$3, 5, 13$

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.

3.48-33.0.2-3-12.4.1

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