K12a940
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+7 q^6-12 q^5+18 q^4-23 q^3+25 q^2-25 q+21-15 q^{-1} +10 q^{-2} -4 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+13 t^2-39 t+57-39 t^{-1} +13 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+z^4-5 z^2+1 }[/math] |
| Determinant | 165 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+a^2 z^4-z^4 a^{-2} +3 z^4 a^{-4} -2 z^4+a^2 z^2-3 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -4 z^2+2 a^2-2 a^{-2} +3 a^{-4} -2 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +7 z^{10} a^{-2} +11 z^{10} a^{-4} +4 z^{10} a^{-6} +13 z^9 a^{-1} +12 z^9 a^{-3} +2 z^9 a^{-5} +3 z^9 a^{-7} -2 z^8 a^{-2} -34 z^8 a^{-4} -15 z^8 a^{-6} +z^8 a^{-8} +16 z^8+15 a z^7-20 z^7 a^{-1} -52 z^7 a^{-3} -31 z^7 a^{-5} -14 z^7 a^{-7} +10 a^2 z^6-30 z^6 a^{-2} +21 z^6 a^{-4} +13 z^6 a^{-6} -5 z^6 a^{-8} -23 z^6+4 a^3 z^5-19 a z^5+4 z^5 a^{-1} +53 z^5 a^{-3} +47 z^5 a^{-5} +21 z^5 a^{-7} +a^4 z^4-9 a^2 z^4+30 z^4 a^{-2} +12 z^4 a^{-4} +4 z^4 a^{-6} +8 z^4 a^{-8} +4 z^4+6 a z^3-7 z^3 a^{-1} -21 z^3 a^{-3} -20 z^3 a^{-5} -12 z^3 a^{-7} +5 a^2 z^2-13 z^2 a^{-2} -12 z^2 a^{-4} -7 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2+a z+5 z a^{-1} +4 z a^{-3} +2 z a^{-5} +2 z a^{-7} -2 a^2+2 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} -1 }[/math] |
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