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

• Label: 9.38-2.0.2-19-38.1
• 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:

$2, 3, 38$

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.

9.38-2.0.2-19-38.1.1

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