K12a821
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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{ 3 a z^{11}+3 z^{11} a^{-1} +8 a^2 z^{10}+8 z^{10} a^{-2} +16 z^{10}+10 a^3 z^9+8 a z^9+8 z^9 a^{-1} +10 z^9 a^{-3} +8 a^4 z^8-17 a^2 z^8-17 z^8 a^{-2} +8 z^8 a^{-4} -50 z^8+4 a^5 z^7-26 a^3 z^7-43 a z^7-43 z^7 a^{-1} -26 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-20 a^4 z^6+13 a^2 z^6+13 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +68 z^6-9 a^5 z^5+24 a^3 z^5+67 a z^5+67 z^5 a^{-1} +24 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+13 a^4 z^4-3 a^2 z^4-3 z^4 a^{-2} +13 z^4 a^{-4} -2 z^4 a^{-6} -36 z^4+3 a^5 z^3-11 a^3 z^3-38 a z^3-38 z^3 a^{-1} -11 z^3 a^{-3} +3 z^3 a^{-5} -3 a^4 z^2-3 z^2 a^{-4} +6 z^2+2 a^3 z+6 a z+6 z a^{-1} +2 z a^{-3} +1 }[/math] |
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