K12n751
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+3 q^6-6 q^5+8 q^4-10 q^3+12 q^2-10 q+9-6 q^{-1} +3 q^{-2} - q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+9 t^2-13 t+15-13 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 69 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +6 z^6 a^{-2} -z^6 a^{-4} -z^6+13 z^4 a^{-2} -4 z^4 a^{-4} -4 z^4+13 z^2 a^{-2} -5 z^2 a^{-4} -5 z^2+6 a^{-2} -3 a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +4 z^9 a^{-3} +3 z^9 a^{-5} -z^8 a^{-2} +2 z^8 a^{-4} +3 z^8 a^{-6} +2 z^7 a^{-1} -8 z^7 a^{-3} -9 z^7 a^{-5} +z^7 a^{-7} +8 z^6 a^{-2} -13 z^6 a^{-4} -12 z^6 a^{-6} +9 z^6+6 a z^5-z^5 a^{-1} -z^5 a^{-3} +2 z^5 a^{-5} -4 z^5 a^{-7} +3 a^2 z^4-25 z^4 a^{-2} +6 z^4 a^{-4} +13 z^4 a^{-6} -15 z^4+a^3 z^3-5 a z^3-8 z^3 a^{-1} +7 z^3 a^{-5} +5 z^3 a^{-7} +18 z^2 a^{-2} +6 z^2 a^{-4} -3 z^2 a^{-6} +9 z^2+2 a z+4 z a^{-1} +3 z a^{-3} -z a^{-5} -2 z a^{-7} -6 a^{-2} -3 a^{-4} -2 }[/math] |
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