K12a510
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-16 q^3+23 q^2-28 q+31-28 q^{-1} +23 q^{-2} -16 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+20 t^2-44 t+57-44 t^{-1} +20 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-4 z^4+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4-z^4 a^{-2} +z^4 a^{-4} -4 z^4+a^4 z^2+z^2 a^{-4} -2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+7 a^3 z^9+15 a z^9+15 z^9 a^{-1} +7 z^9 a^{-3} +7 a^4 z^8+8 a^2 z^8+8 z^8 a^{-2} +7 z^8 a^{-4} +2 z^8+4 a^5 z^7-7 a^3 z^7-28 a z^7-28 z^7 a^{-1} -7 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-29 a^2 z^6-29 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} -28 z^6-9 a^5 z^5-7 a^3 z^5+10 a z^5+10 z^5 a^{-1} -7 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+8 a^4 z^4+22 a^2 z^4+22 z^4 a^{-2} +8 z^4 a^{-4} -2 z^4 a^{-6} +24 z^4+6 a^5 z^3+9 a^3 z^3+7 a z^3+7 z^3 a^{-1} +9 z^3 a^{-3} +6 z^3 a^{-5} +a^6 z^2-2 a^4 z^2-5 a^2 z^2-5 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -4 z^2-a^5 z-3 a^3 z-4 a z-4 z a^{-1} -3 z a^{-3} -z a^{-5} +1 }[/math] |
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