K12a962
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-11 q^6+20 q^5-29 q^4+36 q^3-38 q^2+36 q-28+20 q^{-1} -11 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-28 t^2+51 t-61+51 t^{-1} -28 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+6 z^4+4 z^2+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} +5 z^4-2 a^2 z^2+2 z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2-a^2+2 a^{-2} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +19 z^{10} a^{-2} +11 z^{10} a^{-4} +8 z^{10}+8 a z^9+17 z^9 a^{-1} +26 z^9 a^{-3} +17 z^9 a^{-5} +4 a^2 z^8-34 z^8 a^{-2} -2 z^8 a^{-4} +16 z^8 a^{-6} -12 z^8+a^3 z^7-21 a z^7-66 z^7 a^{-1} -80 z^7 a^{-3} -26 z^7 a^{-5} +10 z^7 a^{-7} -11 a^2 z^6+2 z^6 a^{-2} -30 z^6 a^{-4} -26 z^6 a^{-6} +4 z^6 a^{-8} -9 z^6-3 a^3 z^5+17 a z^5+71 z^5 a^{-1} +79 z^5 a^{-3} +14 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +10 a^2 z^4+13 z^4 a^{-2} +31 z^4 a^{-4} +21 z^4 a^{-6} -3 z^4 a^{-8} +16 z^4+3 a^3 z^3-7 a z^3-38 z^3 a^{-1} -39 z^3 a^{-3} -z^3 a^{-5} +9 z^3 a^{-7} -z^3 a^{-9} -4 a^2 z^2-2 z^2 a^{-2} -9 z^2 a^{-4} -8 z^2 a^{-6} -5 z^2-a^3 z+2 a z+9 z a^{-1} +9 z a^{-3} -3 z a^{-7} +a^2-2 a^{-2} + a^{-6} +1 }[/math] |
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