K12n663
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+6 q^5-11 q^4+16 q^3-18 q^2+19 q-17+13 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-15 t^2+23 t-25+23 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-7 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +6 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-2} +3 z^{10}+6 a z^9+14 z^9 a^{-1} +8 z^9 a^{-3} +4 a^2 z^8+6 z^8 a^{-2} +9 z^8 a^{-4} +z^8+a^3 z^7-20 a z^7-43 z^7 a^{-1} -17 z^7 a^{-3} +5 z^7 a^{-5} -14 a^2 z^6-36 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -28 z^6-3 a^3 z^5+18 a z^5+36 z^5 a^{-1} +10 z^5 a^{-3} -5 z^5 a^{-5} +14 a^2 z^4+36 z^4 a^{-2} +24 z^4 a^{-4} +6 z^4 a^{-6} +32 z^4+2 a^3 z^3-5 a z^3-11 z^3 a^{-1} +7 z^3 a^{-5} +3 z^3 a^{-7} -4 a^2 z^2-13 z^2 a^{-2} -11 z^2 a^{-4} -5 z^2 a^{-6} -11 z^2-z a^{-3} -3 z a^{-5} -2 z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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