K12a1274
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+4 q^3-7 q^2+10 q-12+14 q^{-1} -14 q^{-2} +12 q^{-3} -9 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-13 t^2+17 t-17+17 t^{-1} -13 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-11 z^4-4 z^2+1 }[/math] |
| Determinant | 95 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -6 z^6+4 a^4 z^4-7 a^2 z^4+5 z^4 a^{-2} -13 z^4+4 a^4 z^2-2 a^2 z^2+7 z^2 a^{-2} -13 z^2+a^4+a^2+3 a^{-2} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+2 z^{10} a^{-2} +5 z^{10}+5 a^3 z^9+2 a z^9-z^9 a^{-1} +2 z^9 a^{-3} +6 a^4 z^8-6 a^2 z^8-9 z^8 a^{-2} +z^8 a^{-4} -22 z^8+6 a^5 z^7-12 a^3 z^7-16 a z^7-9 z^7 a^{-1} -11 z^7 a^{-3} +5 a^6 z^6-12 a^4 z^6+a^2 z^6+12 z^6 a^{-2} -6 z^6 a^{-4} +36 z^6+3 a^7 z^5-9 a^5 z^5+12 a^3 z^5+21 a z^5+16 z^5 a^{-1} +19 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+12 a^4 z^4+2 a^2 z^4-9 z^4 a^{-2} +11 z^4 a^{-4} -37 z^4-3 a^7 z^3+6 a^5 z^3-6 a^3 z^3-13 a z^3-10 z^3 a^{-1} -12 z^3 a^{-3} -a^8 z^2+2 a^6 z^2-6 a^4 z^2-a^2 z^2+8 z^2 a^{-2} -6 z^2 a^{-4} +22 z^2-a^5 z+a^3 z+3 a z+3 z a^{-1} +2 z a^{-3} +a^4-a^2-3 a^{-2} -4 }[/math] |
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