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Label Polynomial pp ff ee cc Galois group uu tt Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.3.6.24a1.1 (x3+x+1)6+2(x3+x+1)3+2( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{3} + 2 22 33 66 2424 S3×C6S_3 \times C_6 (as 18T6) 66 33 [2][2] [1][1] [2]36[2]_{3}^{6} [1]36[1]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+2x3+2x^{6} + 2 x^{3} + 2 [3,0][3, 0] [2,1][2, 1] z4+z2+1,z+(t2+t)z^4 + z^2 + 1,z + (t^2 + t) [3,6][3, 6]
2.3.6.24a1.2 (x3+x+1)6+2(x3+x+1)3+6( x^{3} + x + 1 )^{6} + 2 ( x^{3} + x + 1 )^{3} + 6 22 33 66 2424 S3×C6S_3 \times C_6 (as 18T6) 66 33 [2][2] [1][1] [2]36[2]_{3}^{6} [1]36[1]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+2x3+6x^{6} + 2 x^{3} + 6 [3,0][3, 0] [2,1][2, 1] z4+z2+1,z+(t2+t)z^4 + z^2 + 1,z + (t^2 + t) [3,12][3, 12]
2.3.6.33a1.1 (x3+x+1)6+2( x^{3} + x + 1 )^{6} + 2 22 33 66 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [2][2] [3]36[3]_{3}^{6} [2]36[2]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+2x^{6} + 2 [6,0][6, 0] [2,1][2, 1] z4+z2+1,z+tz^4 + z^2 + 1,z + t [3,9][3, 9]
2.3.6.33a1.2 (x3+x+1)6+10( x^{3} + x + 1 )^{6} + 10 22 33 66 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [2][2] [3]36[3]_{3}^{6} [2]36[2]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+10x^{6} + 10 [6,0][6, 0] [2,1][2, 1] z4+z2+1,z+tz^4 + z^2 + 1,z + t [3,9][3, 9]
2.3.6.33a1.25 (x3+x+1)6+4(x3+x+1)3+2( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{3} + 2 22 33 66 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [2][2] [3]36[3]_{3}^{6} [2]36[2]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+4x3+2x^{6} + 4 x^{3} + 2 [6,0][6, 0] [2,1][2, 1] z4+z2+1,z+tz^4 + z^2 + 1,z + t [3,9][3, 9]
2.3.6.33a1.26 (x3+x+1)6+4(x3+x+1)3+10( x^{3} + x + 1 )^{6} + 4 ( x^{3} + x + 1 )^{3} + 10 22 33 66 3333 S3×C6S_3 \times C_6 (as 18T6) 66 33 [3][3] [2][2] [3]36[3]_{3}^{6} [2]36[2]_{3}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+1t^{3} + t + 1 x6+4x3+10x^{6} + 4 x^{3} + 10 [6,0][6, 0] [2,1][2, 1] z4+z2+1,z+tz^4 + z^2 + 1,z + t [3,9][3, 9]
3.6.3.30a1.89 (x6+2x4+x2+2x+2)3+18(x6+2x4+x2+2x+2)+3( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 )^{3} + 18 ( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 ) + 3 33 66 33 3030 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [52][\frac{5}{2}] [32][\frac{3}{2}] not computed not computed not computed not computed t6+2t4+t2+2t+2t^{6} + 2 t^{4} + t^{2} + 2 t + 2 x3+18x+3x^{3} + 18 x + 3 [3,0][3, 0] [1][1] z+(t4+t3+t2+t+1)z + (t^4 + t^3 + t^2 + t + 1) undefined
3.3.6.21a12.1 (x3+2x+1)6+(3x2+6x+3)(x3+2x+1)2+3(x3+2x+1)+3x( x^{3} + 2 x + 1 )^{6} + \left(3 x^{2} + 6 x + 3\right) ( x^{3} + 2 x + 1 )^{2} + 3 ( x^{3} + 2 x + 1 ) + 3 x 33 33 66 2121 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32][\frac{3}{2}] [12][\frac{1}{2}] not computed not computed not computed not computed t3+2t+1t^{3} + 2 t + 1 x6+(3t2+6t+3)x2+3tx^{6} + \left(3 t^{2} + 6 t + 3\right) x^{2} + 3 t [2,0][2, 0] [1,2][1, 2] z3+2,2z2+(2t2+t)z^3 + 2,2 z^2 + (2 t^2 + t) undefined
3.3.6.33a2.63 (x3+2x+1)6+(9x+18)(x3+2x+1)2+(9x+3)(x3+2x+1)+3x( x^{3} + 2 x + 1 )^{6} + \left(9 x + 18\right) ( x^{3} + 2 x + 1 )^{2} + \left(9 x + 3\right) ( x^{3} + 2 x + 1 ) + 3 x 33 33 66 3333 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [52][\frac{5}{2}] [32][\frac{3}{2}] not computed not computed not computed not computed t3+2t+1t^{3} + 2 t + 1 x6+9tx2+3tx^{6} + 9 t x^{2} + 3 t [6,0][6, 0] [1,2][1, 2] z3+2,2z2+(2t2+1)z^3 + 2,2 z^2 + (2 t^2 + 1) undefined
3.2.9.30b2.15 (x2+2x+2)9+6(x2+2x+2)8+3(x2+2x+2)7+6(x2+2x+2)3+21( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{7} + 6 ( x^{2} + 2 x + 2 )^{3} + 21 33 22 99 3030 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32,2][\frac{3}{2}, 2] [12,1][\frac{1}{2},1] not computed not computed not computed not computed t2+2t+2t^{2} + 2 t + 2 x9+6x8+3x7+6x3+21x^{9} + 6 x^{8} + 3 x^{7} + 6 x^{3} + 21 [7,3,0][7, 3, 0] [1,1][1, 1] z3+(t+1),(t+1)z2+(2t+2)z^3 + (t + 1),(t + 1) z^2 + (2 t + 2) undefined
3.2.9.30b6.15 (x2+2x+2)9+6(x2+2x+2)8+6(x2+2x+2)7+3(x2+2x+2)3+21( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{8} + 6 ( x^{2} + 2 x + 2 )^{7} + 3 ( x^{2} + 2 x + 2 )^{3} + 21 33 22 99 3030 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32,2][\frac{3}{2}, 2] [12,1][\frac{1}{2},1] not computed not computed not computed not computed t2+2t+2t^{2} + 2 t + 2 x9+6x8+6x7+3x3+21x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{3} + 21 [7,3,0][7, 3, 0] [1,1][1, 1] z3+(2t+2),(2t+2)z2+(t+1)z^3 + (2 t + 2),(2 t + 2) z^2 + (t + 1) undefined
3.2.9.38c6.9 (x2+2x+2)9+6(x2+2x+2)6+9(x2+2x+2)4+18(x2+2x+2)2+12( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{4} + 18 ( x^{2} + 2 x + 2 )^{2} + 12 33 22 99 3838 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,52][2, \frac{5}{2}] [1,32][1,\frac{3}{2}] not computed not computed not computed not computed t2+2t+2t^{2} + 2 t + 2 x9+6x6+9x4+18x2+12x^{9} + 6 x^{6} + 9 x^{4} + 18 x^{2} + 12 [11,6,0][11, 6, 0] [1,1][1, 1] z6+1,z+(t+1)z^6 + 1,z + (t + 1) undefined
3.2.9.38c6.13 (x2+2x+2)9+6(x2+2x+2)6+18(x2+2x+2)2+21( x^{2} + 2 x + 2 )^{9} + 6 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{2} + 21 33 22 99 3838 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,52][2, \frac{5}{2}] [1,32][1,\frac{3}{2}] not computed not computed not computed not computed t2+2t+2t^{2} + 2 t + 2 x9+6x6+18x2+21x^{9} + 6 x^{6} + 18 x^{2} + 21 [11,6,0][11, 6, 0] [1,1][1, 1] z6+1,z+(t+1)z^6 + 1,z + (t + 1) undefined
3.1.18.31c3.14 x18+6x16+3x14+6x6+12x^{18} + 6 x^{16} + 3 x^{14} + 6 x^{6} + 12 33 11 1818 3131 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32,2][\frac{3}{2}, 2] [12,1][\frac{1}{2},1] not computed not computed not computed not computed t+1t + 1 x18+6x16+3x14+6x6+12x^{18} + 6 x^{16} + 3 x^{14} + 6 x^{6} + 12 [14,6,0][14, 6, 0] [1,2,1][1, 2, 1] z9+2,2z6+2,2z2+1z^9 + 2,2 z^6 + 2,2 z^2 + 1 [1,5,27][1, 5, 27]
3.1.18.31c3.15 x18+6x16+3x14+6x6+21x^{18} + 6 x^{16} + 3 x^{14} + 6 x^{6} + 21 33 11 1818 3131 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32,2][\frac{3}{2}, 2] [12,1][\frac{1}{2},1] not computed not computed not computed not computed t+1t + 1 x18+6x16+3x14+6x6+21x^{18} + 6 x^{16} + 3 x^{14} + 6 x^{6} + 21 [14,6,0][14, 6, 0] [1,2,1][1, 2, 1] z9+2,2z6+2,2z2+1z^9 + 2,2 z^6 + 2,2 z^2 + 1 [1,5,27][1, 5, 27]
3.1.18.31c3.25 x18+3x16+6x14+3x6+6x^{18} + 3 x^{16} + 6 x^{14} + 3 x^{6} + 6 33 11 1818 3131 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [32,2][\frac{3}{2}, 2] [12,1][\frac{1}{2},1] not computed not computed not computed not computed t+1t + 1 x18+3x16+6x14+3x6+6x^{18} + 3 x^{16} + 6 x^{14} + 3 x^{6} + 6 [14,6,0][14, 6, 0] [1,2,1][1, 2, 1] z9+2,2z6+2,2z2+1z^9 + 2,2 z^6 + 2,2 z^2 + 1 undefined
3.1.18.33a1.17 x18+3x16+15x^{18} + 3 x^{16} + 15 33 11 1818 3333 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,2][2, 2] [1,1][1,1] not computed not computed not computed not computed t+1t + 1 x18+3x16+15x^{18} + 3 x^{16} + 15 [16,16,0][16, 16, 0] [1,2][1, 2] z9+2,2z8+1z^9 + 2,2 z^8 + 1 undefined
3.1.18.39c1.43 x18+3x12+9x4+6x^{18} + 3 x^{12} + 9 x^{4} + 6 33 11 1818 3939 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,52][2, \frac{5}{2}] [1,32][1,\frac{3}{2}] not computed not computed not computed not computed t+1t + 1 x18+3x12+9x4+6x^{18} + 3 x^{12} + 9 x^{4} + 6 [22,12,0][22, 12, 0] [1,1,2][1, 1, 2] z9+2,2z6+1,z2+1z^9 + 2,2 z^6 + 1,z^2 + 1 undefined
3.1.18.39c1.44 x18+3x12+9x8+9x4+6x^{18} + 3 x^{12} + 9 x^{8} + 9 x^{4} + 6 33 11 1818 3939 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,52][2, \frac{5}{2}] [1,32][1,\frac{3}{2}] not computed not computed not computed not computed t+1t + 1 x18+3x12+9x8+9x4+6x^{18} + 3 x^{12} + 9 x^{8} + 9 x^{4} + 6 [22,12,0][22, 12, 0] [1,1,2][1, 1, 2] z9+2,2z6+1,z2+1z^9 + 2,2 z^6 + 1,z^2 + 1 undefined
3.1.18.39c1.63 x18+3x12+18x8+9x4+24x^{18} + 3 x^{12} + 18 x^{8} + 9 x^{4} + 24 33 11 1818 3939 S3×C6S_3 \times C_6 (as 18T6) not computed not computed [2,52][2, \frac{5}{2}] [1,32][1,\frac{3}{2}] not computed not computed not computed not computed t+1t + 1 x18+3x12+18x8+9x4+24x^{18} + 3 x^{12} + 18 x^{8} + 9 x^{4} + 24 [22,12,0][22, 12, 0] [1,1,2][1, 1, 2] z9+2,2z6+1,z2+1z^9 + 2,2 z^6 + 1,z^2 + 1 undefined
5.3.6.15a1.1 (x3+3x+3)6+5x( x^{3} + 3 x + 3 )^{6} + 5 x 55 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+3t^{3} + 3 t + 3 x6+5tx^{6} + 5 t [0][0] [2][2] z5+z4+1z^5 + z^4 + 1 undefined
5.3.6.15a1.2 (x3+3x+3)6+5( x^{3} + 3 x + 3 )^{6} + 5 55 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+3t^{3} + 3 t + 3 x6+5x^{6} + 5 [0][0] [2][2] z5+z4+1z^5 + z^4 + 1 undefined
11.3.6.15a1.1 (x3+2x+9)6+11x( x^{3} + 2 x + 9 )^{6} + 11 x 1111 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+9t^{3} + 2 t + 9 x6+11tx^{6} + 11 t [0][0] [2][2] z5+6z4+4z3+9z2+4z+6z^5 + 6 z^4 + 4 z^3 + 9 z^2 + 4 z + 6 undefined
11.3.6.15a1.2 (x3+2x+9)6+11( x^{3} + 2 x + 9 )^{6} + 11 1111 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+9t^{3} + 2 t + 9 x6+11x^{6} + 11 [0][0] [2][2] z5+6z4+4z3+9z2+4z+6z^5 + 6 z^4 + 4 z^3 + 9 z^2 + 4 z + 6 undefined
17.3.6.15a1.1 (x3+x+14)6+17x( x^{3} + x + 14 )^{6} + 17 x 1717 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+14t^{3} + t + 14 x6+17tx^{6} + 17 t [0][0] [2][2] z5+6z4+15z3+3z2+15z+6z^5 + 6 z^4 + 15 z^3 + 3 z^2 + 15 z + 6 undefined
17.3.6.15a1.2 (x3+x+14)6+17( x^{3} + x + 14 )^{6} + 17 1717 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+14t^{3} + t + 14 x6+17x^{6} + 17 [0][0] [2][2] z5+6z4+15z3+3z2+15z+6z^5 + 6 z^4 + 15 z^3 + 3 z^2 + 15 z + 6 undefined
23.3.6.15a1.1 (x3+2x+18)6+23x( x^{3} + 2 x + 18 )^{6} + 23 x 2323 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+18t^{3} + 2 t + 18 x6+23tx^{6} + 23 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
23.3.6.15a1.2 (x3+2x+18)6+23( x^{3} + 2 x + 18 )^{6} + 23 2323 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+18t^{3} + 2 t + 18 x6+23x^{6} + 23 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
29.3.6.15a1.1 (x3+2x+27)6+29x( x^{3} + 2 x + 27 )^{6} + 29 x 2929 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+27t^{3} + 2 t + 27 x6+29tx^{6} + 29 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
29.3.6.15a1.2 (x3+2x+27)6+29( x^{3} + 2 x + 27 )^{6} + 29 2929 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+2t+27t^{3} + 2 t + 27 x6+29x^{6} + 29 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
41.3.6.15a1.1 (x3+x+35)6+41x( x^{3} + x + 35 )^{6} + 41 x 4141 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+35t^{3} + t + 35 x6+41tx^{6} + 41 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
41.3.6.15a1.2 (x3+x+35)6+41( x^{3} + x + 35 )^{6} + 41 4141 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+t+35t^{3} + t + 35 x6+41x^{6} + 41 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
47.3.6.15a1.1 (x3+3x+42)6+47x( x^{3} + 3 x + 42 )^{6} + 47 x 4747 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+42t^{3} + 3 t + 42 x6+47tx^{6} + 47 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
47.3.6.15a1.2 (x3+3x+42)6+47( x^{3} + 3 x + 42 )^{6} + 47 4747 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+42t^{3} + 3 t + 42 x6+47x^{6} + 47 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
53.3.6.15a1.1 (x3+3x+51)6+53x( x^{3} + 3 x + 51 )^{6} + 53 x 5353 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+51t^{3} + 3 t + 51 x6+53tx^{6} + 53 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
53.3.6.15a1.2 (x3+3x+51)6+53( x^{3} + 3 x + 51 )^{6} + 53 5353 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+51t^{3} + 3 t + 51 x6+53x^{6} + 53 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
59.3.6.15a1.1 (x3+5x+57)6+59x( x^{3} + 5 x + 57 )^{6} + 59 x 5959 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+5t+57t^{3} + 5 t + 57 x6+59tx^{6} + 59 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
59.3.6.15a1.2 (x3+5x+57)6+59( x^{3} + 5 x + 57 )^{6} + 59 5959 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+5t+57t^{3} + 5 t + 57 x6+59x^{6} + 59 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
71.3.6.15a1.1 (x3+4x+64)6+71x( x^{3} + 4 x + 64 )^{6} + 71 x 7171 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+4t+64t^{3} + 4 t + 64 x6+71tx^{6} + 71 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
71.3.6.15a1.2 (x3+4x+64)6+71( x^{3} + 4 x + 64 )^{6} + 71 7171 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+4t+64t^{3} + 4 t + 64 x6+71x^{6} + 71 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
83.3.6.15a1.1 (x3+3x+81)6+83x( x^{3} + 3 x + 81 )^{6} + 83 x 8383 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+81t^{3} + 3 t + 81 x6+83tx^{6} + 83 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
83.3.6.15a1.2 (x3+3x+81)6+83( x^{3} + 3 x + 81 )^{6} + 83 8383 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+81t^{3} + 3 t + 81 x6+83x^{6} + 83 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
89.3.6.15a1.1 (x3+3x+86)6+89x( x^{3} + 3 x + 86 )^{6} + 89 x 8989 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+86t^{3} + 3 t + 86 x6+89tx^{6} + 89 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
89.3.6.15a1.2 (x3+3x+86)6+89( x^{3} + 3 x + 86 )^{6} + 89 8989 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+86t^{3} + 3 t + 86 x6+89x^{6} + 89 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
101.3.6.15a1.1 (x3+3x+99)6+101x( x^{3} + 3 x + 99 )^{6} + 101 x 101101 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+99t^{3} + 3 t + 99 x6+101tx^{6} + 101 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
101.3.6.15a1.2 (x3+3x+99)6+101( x^{3} + 3 x + 99 )^{6} + 101 101101 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+3t+99t^{3} + 3 t + 99 x6+101x^{6} + 101 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
107.3.6.15a1.1 (x3+5x+105)6+107x( x^{3} + 5 x + 105 )^{6} + 107 x 107107 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+5t+105t^{3} + 5 t + 105 x6+107tx^{6} + 107 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
107.3.6.15a1.2 (x3+5x+105)6+107( x^{3} + 5 x + 105 )^{6} + 107 107107 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+5t+105t^{3} + 5 t + 105 x6+107x^{6} + 107 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
113.3.6.15a1.1 (x3+8x+110)6+113x( x^{3} + 8 x + 110 )^{6} + 113 x 113113 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+8t+110t^{3} + 8 t + 110 x6+113tx^{6} + 113 t [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
113.3.6.15a1.2 (x3+8x+110)6+113( x^{3} + 8 x + 110 )^{6} + 113 113113 33 66 1515 S3×C6S_3 \times C_6 (as 18T6) 66 66 [ ][\ ] [ ][\ ] [ ]66[\ ]_{6}^{6} [ ]66[\ ]_{6}^{6} [ ]2[\ ]^{2} [ ]2[\ ]^{2} t3+8t+110t^{3} + 8 t + 110 x6+113x^{6} + 113 [0][0] [2][2] z5+6z4+15z3+20z2+15z+6z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6 undefined
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