One refined passport of genus 12 with automorphism group $C_{50}$

• Label: 12.50-2.0.2-25-50.4
• Genus: \(12\)
• Quotient genus: \(0\)
• Group: \(C_{50}\)
• Signature: \([ 0; 2, 25, 50 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$12$
Quotient genus:	$0$
Group name:	$C_{50}$
Group identifier:	$[50,2]$
Signature:	$[ 0; 2, 25, 50 ]$

Conjugacy classes for this refined passport:

$2, 14, 39$

Jacobian variety group algebra decomposition:

$A_{10}\times A_{2}$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
Cyclic trigonal curve(s):	no

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

$y^2=x^{25}+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

12.50-2.0.2-25-50.4.1

	(1,26) (2,27) (3,28) (4,29) (5,30) (6,31) (7,32) (8,33) (9,34) (10,35) (11,36) (12,37) (13,38) (14,39) (15,40) (16,41) (17,42) (18,43) (19,44) (20,45) (21,46) (22,47) (23,48) (24,49) (25,50)
	(1,21,17,13,9,5,25,16,12,8,4,24,20,11,7,3,23,19,15,6,2,22,18,14,10) (26,46,42,38,34,30,50,41,37,33,29,49,45,36,32,28,48,44,40,31,27,47,43,39,35)
	(1,35,14,43,22,27,6,40,19,48,3,32,11,45,24,29,8,37,16,50,5,34,13,42,21,26,10,39,18,47,2,31,15,44,23,28,7,36,20,49,4,33,12,41,25,30,9,38,17,46)