One refined passport of genus 14 with automorphism group $\SL(2,5)$

• Label: 14.120-5.0.3-4-5.1
• Genus: \(14\)
• Quotient genus: \(0\)
• Group: \(\SL(2,5)\)
• Signature: \([ 0; 3, 4, 5 ]\)
• Generating Vectors: \(1\)

Family Information

Genus:	$14$
Quotient genus:	$0$
Group name:	$\SL(2,5)$
Group identifier:	$[120,5]$
Signature:	$[ 0; 3, 4, 5 ]$

Conjugacy classes for this refined passport:

$3, 4, 5$

Jacobian variety group algebra decomposition:	$A_{4}\times A_{2}^{2}\times A_{2}^{3}$
Corresponding character(s):	$2, 6, 9$

Other Data

Hyperelliptic curve(s):	yes
Hyperelliptic involution:	(1,6) (2,4) (3,13) (5,14) (7,33) (8,10) (9,103) (11,12) (15,16) (17,19) (18,20) (21,23) (22,24) (25,30) (26,28) (27,37) (29,38) (31,57) (32,34) (35,36) (39,40) (41,43) (42,44) (45,47) (46,48) (49,54) (50,52) (51,61) (53,62) (55,81) (56,58) (59,60) (63,64) (65,67) (66,68) (69,71) (70,72) (73,78) (74,76) (75,85) (77,86) (79,105) (80,82) (83,84) (87,88) (89,91) (90,92) (93,95) (94,96) (97,102) (98,100) (99,109) (101,110) (104,106) (107,108) (111,112) (113,115) (114,116) (117,119) (118,120)
Cyclic trigonal curve(s):	no

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

$y^2=x^{30}+522x^{25}-10005x^{20}-10005x^{15}-522x^5+1$

Generating vector(s)

Displaying the unique generating vector for this refined passport.

14.120-5.0.3-4-5.1.1

	(1,3,5) (2,7,8) (4,33,10) (6,13,14) (9,106,100) (11,17,18) (12,19,20) (15,21,22) (16,23,24) (25,27,29) (26,31,32) (28,57,34) (30,37,38) (35,41,42) (36,43,44) (39,45,46) (40,47,48) (49,51,53) (50,55,56) (52,81,58) (54,61,62) (59,65,66) (60,67,68) (63,69,70) (64,71,72) (73,75,77) (74,79,80) (76,105,82) (78,85,86) (83,89,90) (84,91,92) (87,93,94) (88,95,96) (97,99,101) (98,103,104) (102,109,110) (107,113,114) (108,115,116) (111,117,118) (112,119,120)
	(1,71,6,69) (2,89,4,91) (3,86,13,77) (5,51,14,61) (7,58,33,56) (8,79,10,105) (9,32,103,34) (11,87,12,88) (15,60,16,59) (17,52,19,50) (18,48,20,46) (21,73,23,78) (22,114,24,116) (25,95,30,93) (26,113,28,115) (27,110,37,101) (29,75,38,85) (31,82,57,80) (35,111,36,112) (39,84,40,83) (41,76,43,74) (42,72,44,70) (45,97,47,102) (49,119,54,117) (53,99,62,109) (55,106,81,104) (63,108,64,107) (65,100,67,98) (66,96,68,94) (90,120,92,118)
	(1,63,114,21,86) (2,84,46,19,58) (3,75,27,99,51) (4,83,48,17,56) (5,54,112,44,71) (6,64,116,23,77) (7,55,103,31,79) (8,76,35,120,89) (9,57,105,33,81) (10,74,36,118,91) (11,96,65,104,52) (12,94,67,106,50) (13,85,37,109,61) (14,49,111,42,69) (15,66,93,38,73) (16,68,95,29,78) (18,45,110,25,87) (20,47,101,30,88) (22,115,34,98,60) (24,113,32,100,59) (26,108,70,43,82) (28,107,72,41,80) (39,90,117,62,97) (40,92,119,53,102)