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

• Label: 9.38-2.0.2-19-38.10
• 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:

$2, 12, 25$

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.

9.38-2.0.2-19-38.10.1

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