K12n156
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+2 q^6-3 q^5+5 q^4-5 q^3+5 q^2-5 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+8 t^2-3 t-1-3 t^{-1} +8 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-2 z^4+1 }[/math] |
| Determinant | 33 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -10 z^4 a^{-2} +12 z^4 a^{-4} -5 z^4 a^{-6} +z^4-13 z^2 a^{-2} +13 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +4 z^2-6 a^{-2} +6 a^{-4} -2 a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} -z^8 a^{-2} +z^8 a^{-4} +3 z^8 a^{-6} +z^8-11 z^7 a^{-1} -26 z^7 a^{-3} -14 z^7 a^{-5} +z^7 a^{-7} -17 z^6 a^{-2} -27 z^6 a^{-4} -16 z^6 a^{-6} -6 z^6+18 z^5 a^{-1} +36 z^5 a^{-3} +13 z^5 a^{-5} -5 z^5 a^{-7} +40 z^4 a^{-2} +51 z^4 a^{-4} +23 z^4 a^{-6} +12 z^4-11 z^3 a^{-1} -15 z^3 a^{-3} +z^3 a^{-5} +5 z^3 a^{-7} -29 z^2 a^{-2} -31 z^2 a^{-4} -13 z^2 a^{-6} -z^2 a^{-8} -10 z^2+2 z a^{-1} +2 z a^{-3} -2 z a^{-5} -2 z a^{-7} +6 a^{-2} +6 a^{-4} +2 a^{-6} +3 }[/math] |
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