K12a136
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+18 q-26+32 q^{-1} -35 q^{-2} +33 q^{-3} -27 q^{-4} +19 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-26 t^2+47 t-55+47 t^{-1} -26 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+2 z^4-z^2+1 }[/math] |
| Determinant | 219 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+6 a^4 z^4-8 a^2 z^4-z^4 a^{-2} +6 z^4-2 a^6 z^2+7 a^4 z^2-10 a^2 z^2-2 z^2 a^{-2} +6 z^2-a^6+4 a^4-5 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+8 a^4 z^{10}+14 a^2 z^{10}+6 z^{10}+14 a^5 z^9+24 a^3 z^9+17 a z^9+7 z^9 a^{-1} +14 a^6 z^8+8 a^4 z^8-15 a^2 z^8+4 z^8 a^{-2} -5 z^8+9 a^7 z^7-18 a^5 z^7-66 a^3 z^7-60 a z^7-20 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-22 a^6 z^6-48 a^4 z^6-33 a^2 z^6-13 z^6 a^{-2} -24 z^6+a^9 z^5-11 a^7 z^5+6 a^5 z^5+58 a^3 z^5+61 a z^5+18 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+18 a^6 z^4+53 a^4 z^4+56 a^2 z^4+14 z^4 a^{-2} +39 z^4-a^9 z^3+6 a^7 z^3+a^5 z^3-26 a^3 z^3-29 a z^3-7 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-7 a^6 z^2-25 a^4 z^2-31 a^2 z^2-6 z^2 a^{-2} -20 z^2-a^7 z+6 a^3 z+7 a z+2 z a^{-1} +a^6+4 a^4+5 a^2+3 }[/math] |
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