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

• Label: 12.50-2.0.2-25-50.10
• 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:

$2, 20, 36$

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.

12.50-2.0.2-25-50.10.1

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