K12a1165
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+4 q^7-6 q^6+8 q^5-10 q^4+10 q^3-9 q^2+7 q-5+3 q^{-1} - q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -6 t^2+17 t-21+17 t^{-1} -6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -6 z^4-7 z^2+1 }[/math] |
| Determinant | 67 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^4 a^{-2} -2 z^4 a^{-4} -z^4 a^{-6} -z^4+a^2 z^2-3 z^2 a^{-2} -3 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -2 z^2+2 a^2- a^{-4} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10} a^{-6} +z^9 a^{-1} -6 z^9 a^{-3} -4 z^9 a^{-5} +3 z^9 a^{-7} -4 z^8 a^{-2} -16 z^8 a^{-4} -8 z^8 a^{-6} +3 z^8 a^{-8} +z^8+a z^7-3 z^7 a^{-1} +19 z^7 a^{-3} +8 z^7 a^{-5} -13 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6+9 z^6 a^{-2} +36 z^6 a^{-4} +11 z^6 a^{-6} -12 z^6 a^{-8} +z^6 a^{-10} -2 z^6-3 a z^5+6 z^5 a^{-1} -28 z^5 a^{-3} -10 z^5 a^{-5} +20 z^5 a^{-7} -7 z^5 a^{-9} -5 a^2 z^4-7 z^4 a^{-2} -33 z^4 a^{-4} -4 z^4 a^{-6} +14 z^4 a^{-8} -4 z^4 a^{-10} -z^4+a z^3-8 z^3 a^{-1} +22 z^3 a^{-3} +13 z^3 a^{-5} -14 z^3 a^{-7} +4 z^3 a^{-9} +7 a^2 z^2-z^2 a^{-2} +15 z^2 a^{-4} -8 z^2 a^{-8} +3 z^2 a^{-10} +2 z^2+a z+z a^{-1} -6 z a^{-3} -4 z a^{-5} +2 z a^{-7} -2 a^2- a^{-4} + a^{-8} -1 }[/math] |
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