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

• Label: 14.120-5.0.3-4-5.2
• 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:

$3, 4, 6$

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.

14.120-5.0.3-4-5.2.1

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