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

• Label: 9.38-2.0.2-19-38.4
• 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:

$2, 6, 28$

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.

9.38-2.0.2-19-38.4.1

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