K12a1195
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+19 q^5-28 q^4+35 q^3-38 q^2+36 q-29+21 q^{-1} -12 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-29 t^2+51 t-59+51 t^{-1} -29 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+5 z^4+1 }[/math] |
| Determinant | 239 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-2 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +4 z^4-a^2 z^2+2 z^2 a^{-2} +2 z^2 a^{-4} -2 z^2 a^{-6} -z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +22 z^{10} a^{-2} +12 z^{10} a^{-4} +10 z^{10}+10 a z^9+13 z^9 a^{-1} +19 z^9 a^{-3} +16 z^9 a^{-5} +5 a^2 z^8-53 z^8 a^{-2} -14 z^8 a^{-4} +14 z^8 a^{-6} -20 z^8+a^3 z^7-27 a z^7-60 z^7 a^{-1} -69 z^7 a^{-3} -28 z^7 a^{-5} +9 z^7 a^{-7} -13 a^2 z^6+40 z^6 a^{-2} -21 z^6 a^{-6} +4 z^6 a^{-8} +2 z^6-2 a^3 z^5+19 a z^5+59 z^5 a^{-1} +75 z^5 a^{-3} +25 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +9 a^2 z^4-20 z^4 a^{-2} +4 z^4 a^{-4} +14 z^4 a^{-6} -4 z^4 a^{-8} +3 z^4+a^3 z^3-4 a z^3-24 z^3 a^{-1} -38 z^3 a^{-3} -13 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} -a^2 z^2+11 z^2 a^{-2} -3 z^2 a^{-6} +z^2 a^{-8} +6 z^2+a z+5 z a^{-1} +7 z a^{-3} +3 z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math] |
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