K12a61
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+16 q^5-23 q^4+27 q^3-28 q^2+26 q-20+14 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-21 t^2+38 t-45+38 t^{-1} -21 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+z^4+z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-12 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +8 z^4-3 a^2 z^2-15 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} +12 z^2-2 a^2-7 a^{-2} +4 a^{-4} - a^{-6} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +7 z^{10} a^{-2} +4 z^{10} a^{-4} +3 z^{10}+4 a z^9+10 z^9 a^{-1} +14 z^9 a^{-3} +8 z^9 a^{-5} +3 a^2 z^8+2 z^8 a^{-2} +13 z^8 a^{-4} +10 z^8 a^{-6} +2 z^8+a^3 z^7-9 a z^7-25 z^7 a^{-1} -22 z^7 a^{-3} +z^7 a^{-5} +8 z^7 a^{-7} -11 a^2 z^6-39 z^6 a^{-2} -38 z^6 a^{-4} -11 z^6 a^{-6} +4 z^6 a^{-8} -27 z^6-4 a^3 z^5+7 z^5 a^{-1} -7 z^5 a^{-3} -22 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+48 z^4 a^{-2} +31 z^4 a^{-4} +3 z^4 a^{-6} -5 z^4 a^{-8} +39 z^4+5 a^3 z^3+10 a z^3+12 z^3 a^{-1} +20 z^3 a^{-3} +21 z^3 a^{-5} +7 z^3 a^{-7} -z^3 a^{-9} -8 a^2 z^2-28 z^2 a^{-2} -14 z^2 a^{-4} +2 z^2 a^{-8} -24 z^2-2 a^3 z-5 a z-7 z a^{-1} -8 z a^{-3} -6 z a^{-5} -2 z a^{-7} +2 a^2+7 a^{-2} +4 a^{-4} + a^{-6} +7 }[/math] |
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