K12a1266
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-3 q^9+7 q^8-11 q^7+15 q^6-19 q^5+19 q^4-18 q^3+15 q^2-10 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+15 t^2-28 t+35-28 t^{-1} +15 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-9 z^4-4 z^2+1 }[/math] |
| Determinant | 129 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -2 z^6 a^{-4} -z^6 a^{-6} -2 z^4 a^{-2} -7 z^4 a^{-4} -2 z^4 a^{-6} +z^4 a^{-8} +z^4+z^2 a^{-2} -9 z^2 a^{-4} +2 z^2 a^{-8} +2 z^2+3 a^{-2} -5 a^{-4} + a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +10 z^{10} a^{-4} +6 z^{10} a^{-6} +3 z^9 a^{-1} -z^9 a^{-3} +5 z^9 a^{-5} +9 z^9 a^{-7} -17 z^8 a^{-2} -41 z^8 a^{-4} -14 z^8 a^{-6} +9 z^8 a^{-8} +z^8-14 z^7 a^{-1} -22 z^7 a^{-3} -41 z^7 a^{-5} -25 z^7 a^{-7} +8 z^7 a^{-9} +20 z^6 a^{-2} +54 z^6 a^{-4} +6 z^6 a^{-6} -17 z^6 a^{-8} +6 z^6 a^{-10} -5 z^6+19 z^5 a^{-1} +37 z^5 a^{-3} +66 z^5 a^{-5} +34 z^5 a^{-7} -11 z^5 a^{-9} +3 z^5 a^{-11} -9 z^4 a^{-2} -36 z^4 a^{-4} +3 z^4 a^{-6} +14 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +8 z^4-8 z^3 a^{-1} -19 z^3 a^{-3} -50 z^3 a^{-5} -31 z^3 a^{-7} +6 z^3 a^{-9} -2 z^3 a^{-11} +6 z^2 a^{-2} +18 z^2 a^{-4} -5 z^2 a^{-6} -7 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} -5 z^2+6 z a^{-3} +16 z a^{-5} +10 z a^{-7} -3 a^{-2} -5 a^{-4} - a^{-6} + a^{-8} +1 }[/math] |
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