K12a873
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+8 q^6-15 q^5+22 q^4-26 q^3+30 q^2-28 q+23-17 q^{-1} +10 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^3+22 t^2-42 t+51-42 t^{-1} +22 t^{-2} -5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -5 z^6-8 z^4+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -3 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-10 z^4 a^{-2} +z^4 a^{-6} +a^2 z^2-11 z^2 a^{-2} +6 z^2 a^{-4} +z^2 a^{-6} +4 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +8 z^{10} a^{-2} +13 z^{10} a^{-4} +5 z^{10} a^{-6} +16 z^9 a^{-1} +20 z^9 a^{-3} +8 z^9 a^{-5} +4 z^9 a^{-7} +6 z^8 a^{-2} -32 z^8 a^{-4} -17 z^8 a^{-6} +z^8 a^{-8} +20 z^8+17 a z^7-22 z^7 a^{-1} -73 z^7 a^{-3} -52 z^7 a^{-5} -18 z^7 a^{-7} +10 a^2 z^6-60 z^6 a^{-2} +z^6 a^{-4} +13 z^6 a^{-6} -4 z^6 a^{-8} -34 z^6+4 a^3 z^5-23 a z^5-6 z^5 a^{-1} +64 z^5 a^{-3} +70 z^5 a^{-5} +27 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+58 z^4 a^{-2} +31 z^4 a^{-4} +5 z^4 a^{-6} +5 z^4 a^{-8} +19 z^4+12 a z^3+7 z^3 a^{-1} -18 z^3 a^{-3} -26 z^3 a^{-5} -13 z^3 a^{-7} +3 a^2 z^2-23 z^2 a^{-2} -15 z^2 a^{-4} -5 z^2 a^{-6} -2 z^2 a^{-8} -8 z^2-2 a z-3 z a^{-1} -z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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