K12n71
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+8 q^3-9 q^2+10 q-8+7 q^{-1} -4 q^{-2} +2 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-9 t^2+10 t-9+10 t^{-1} -9 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 59 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-13 z^4 a^{-2} +5 z^4 a^{-4} +10 z^4-4 a^2 z^2-14 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +15 z^2-3 a^2-6 a^{-2} +3 a^{-4} - a^{-6} +8 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+2 a z^9+5 z^9 a^{-1} +3 z^9 a^{-3} +2 a^2 z^8+2 z^8 a^{-2} +3 z^8 a^{-4} +z^8+a^3 z^7-6 a z^7-19 z^7 a^{-1} -11 z^7 a^{-3} +z^7 a^{-5} -9 a^2 z^6-20 z^6 a^{-2} -11 z^6 a^{-4} -18 z^6-5 a^3 z^5-a z^5+20 z^5 a^{-1} +16 z^5 a^{-3} +12 a^2 z^4+36 z^4 a^{-2} +20 z^4 a^{-4} +3 z^4 a^{-6} +31 z^4+7 a^3 z^3+9 a z^3-6 z^3 a^{-1} -8 z^3 a^{-3} +z^3 a^{-5} +z^3 a^{-7} -8 a^2 z^2-26 z^2 a^{-2} -13 z^2 a^{-4} -3 z^2 a^{-6} -24 z^2-3 a^3 z-5 a z-2 z a^{-1} +z a^{-3} -z a^{-7} +3 a^2+6 a^{-2} +3 a^{-4} + a^{-6} +8 }[/math] |
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