K12a324
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+19 q-27+34 q^{-1} -36 q^{-2} +34 q^{-3} -28 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+49 t-59+49 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 | 227 |
| 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^2-9 a^2 z^2-2 z^2 a^{-2} +7 z^2-a^6+3 a^4-4 a^2- a^{-2} +4 }[/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+25 a^3 z^9+18 a z^9+7 z^9 a^{-1} +14 a^6 z^8+11 a^4 z^8-9 a^2 z^8+4 z^8 a^{-2} -2 z^8+9 a^7 z^7-15 a^5 z^7-60 a^3 z^7-54 a z^7-17 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-21 a^6 z^6-53 a^4 z^6-45 a^2 z^6-12 z^6 a^{-2} -29 z^6+a^9 z^5-11 a^7 z^5-2 a^5 z^5+34 a^3 z^5+37 a z^5+10 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+17 a^6 z^4+52 a^4 z^4+56 a^2 z^4+13 z^4 a^{-2} +38 z^4-a^9 z^3+7 a^7 z^3+11 a^5 z^3-a^3 z^3-5 a z^3+2 z^3 a^{-1} +3 z^3 a^{-3} +a^8 z^2-6 a^6 z^2-20 a^4 z^2-25 a^2 z^2-6 z^2 a^{-2} -18 z^2-2 a^7 z-4 a^5 z-3 a^3 z-2 a z-2 z a^{-1} -z a^{-3} +a^6+3 a^4+4 a^2+ a^{-2} +4 }[/math] |
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