One refined passport of genus 9 with automorphism group $C_{38}$

• Label: 9.38-2.0.2-19-38.12
• Genus: \(9\)
• Quotient genus: \(0\)
• Group: \(C_{38}\)
• Signature: \([ 0; 2, 19, 38 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$9$
Quotient genus:	$0$
Group name:	$C_{38}$
Group identifier:	$[38,2]$
Signature:	$[ 0; 2, 19, 38 ]$

Conjugacy classes for this refined passport:

$2, 14, 24$

Jacobian variety group algebra decomposition:

$A_{9}$

Other Data

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

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

$y^2=x^{19}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

9.38-2.0.2-19-38.12.1

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