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

• Label: 9.38-2.0.2-19-38.16
• 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:

$2, 18, 22$

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.

9.38-2.0.2-19-38.16.1

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