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

• Label: 12.50-2.0.2-25-50.13
• 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:

$2, 23, 34$

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.

12.50-2.0.2-25-50.13.1

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