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

• Label: 3.48-33.0.2-3-12.3
• 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:

$3, 5, 11$

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.

3.48-33.0.2-3-12.3.1

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