K12a446
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+20 q^5-29 q^4+35 q^3-36 q^2+34 q-26+18 q^{-1} -10 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-26 t^2+50 t-61+50 t^{-1} -26 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+2 z^4+2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-4 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +6 z^2-a^2+ a^{-2} - a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +14 z^{10} a^{-2} +8 z^{10} a^{-4} +6 z^{10}+7 a z^9+17 z^9 a^{-1} +25 z^9 a^{-3} +15 z^9 a^{-5} +4 a^2 z^8-11 z^8 a^{-2} +14 z^8 a^{-4} +17 z^8 a^{-6} -4 z^8+a^3 z^7-18 a z^7-53 z^7 a^{-1} -57 z^7 a^{-3} -11 z^7 a^{-5} +12 z^7 a^{-7} -12 a^2 z^6-36 z^6 a^{-2} -53 z^6 a^{-4} -23 z^6 a^{-6} +5 z^6 a^{-8} -23 z^6-3 a^3 z^5+12 a z^5+42 z^5 a^{-1} +31 z^5 a^{-3} -11 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4+44 z^4 a^{-2} +38 z^4 a^{-4} +11 z^4 a^{-6} -3 z^4 a^{-8} +32 z^4+3 a^3 z^3-10 z^3 a^{-1} -6 z^3 a^{-3} +6 z^3 a^{-5} +5 z^3 a^{-7} -5 a^2 z^2-13 z^2 a^{-2} -8 z^2 a^{-4} -3 z^2 a^{-6} -13 z^2-a^3 z-a z+z a^{-1} +3 z a^{-3} +2 z a^{-5} +a^2- a^{-2} - a^{-4} +2 }[/math] |
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