K12a1276
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+4 q^3-6 q^2+8 q-10+11 q^{-1} -10 q^{-2} +9 q^{-3} -7 q^{-4} +4 q^{-5} -2 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+6 t^3-10 t^2+13 t-13+13 t^{-1} -10 t^{-2} +6 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-10 z^6-14 z^4-5 z^2+1 }[/math] |
| Determinant | 75 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-6 a^2 z^6+z^6 a^{-2} -6 z^6+5 a^4 z^4-12 a^2 z^4+5 z^4 a^{-2} -12 z^4+7 a^4 z^2-9 a^2 z^2+7 z^2 a^{-2} -10 z^2+2 a^4-a^2+3 a^{-2} -3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+2 z^{10} a^{-2} +4 z^{10}+3 a^3 z^9-2 a z^9-3 z^9 a^{-1} +2 z^9 a^{-3} +4 a^4 z^8-5 a^2 z^8-10 z^8 a^{-2} +z^8 a^{-4} -20 z^8+4 a^5 z^7-8 a^3 z^7+z^7 a^{-1} -11 z^7 a^{-3} +3 a^6 z^6-12 a^4 z^6+2 a^2 z^6+16 z^6 a^{-2} -6 z^6 a^{-4} +39 z^6+2 a^7 z^5-10 a^5 z^5+8 a^3 z^5-2 z^5 a^{-1} +18 z^5 a^{-3} +a^8 z^4-5 a^6 z^4+18 a^4 z^4+6 a^2 z^4-14 z^4 a^{-2} +11 z^4 a^{-4} -43 z^4-3 a^7 z^3+12 a^5 z^3-a^3 z^3-3 a z^3+4 z^3 a^{-1} -9 z^3 a^{-3} -2 a^8 z^2+3 a^6 z^2-9 a^4 z^2-10 a^2 z^2+11 z^2 a^{-2} -6 z^2 a^{-4} +21 z^2-2 a^5 z-a^3 z+z a^{-3} +2 a^4+a^2-3 a^{-2} -3 }[/math] |
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