K12a1012
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+9 q^5-15 q^4+21 q^3-24 q^2+25 q-23+18 q^{-1} -12 q^{-2} +7 q^{-3} -3 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-21 t^2+32 t-35+32 t^{-1} -21 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-7 z^4-3 z^2+1 }[/math] |
| Determinant | 163 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-4 z^6 a^{-2} +z^6 a^{-4} -5 z^6+4 a^2 z^4-4 z^4 a^{-2} +3 z^4 a^{-4} -10 z^4+5 a^2 z^2+z^2 a^{-2} +2 z^2 a^{-4} -11 z^2+3 a^2+3 a^{-2} -5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+7 z^{10} a^{-2} +11 z^{10}+3 a^3 z^9+a z^9+11 z^9 a^{-1} +13 z^9 a^{-3} +a^4 z^8-16 a^2 z^8-4 z^8 a^{-2} +16 z^8 a^{-4} -37 z^8-14 a^3 z^7-25 a z^7-47 z^7 a^{-1} -22 z^7 a^{-3} +14 z^7 a^{-5} -5 a^4 z^6+20 a^2 z^6-20 z^6 a^{-2} -27 z^6 a^{-4} +9 z^6 a^{-6} +41 z^6+21 a^3 z^5+38 a z^5+46 z^5 a^{-1} +7 z^5 a^{-3} -18 z^5 a^{-5} +4 z^5 a^{-7} +8 a^4 z^4-11 a^2 z^4+10 z^4 a^{-2} +13 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} -30 z^4-11 a^3 z^3-18 a z^3-19 z^3 a^{-1} -4 z^3 a^{-3} +7 z^3 a^{-5} -z^3 a^{-7} -4 a^4 z^2+7 a^2 z^2+5 z^2 a^{-2} -2 z^2 a^{-4} +2 z^2 a^{-6} +20 z^2+2 a^3 z+3 a z+3 z a^{-1} +2 z a^{-3} -3 a^2-3 a^{-2} -5 }[/math] |
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