K12a414
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-4 q^{10}+8 q^9-13 q^8+18 q^7-21 q^6+22 q^5-21 q^4+17 q^3-11 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -9 t^2+37 t-55+37 t^{-1} -9 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -9 z^4+z^2+1 }[/math] |
| Determinant | 147 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^{-2} -3 z^4 a^{-4} -4 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-4} -5 z^2 a^{-6} +3 z^2 a^{-8} +z^2 a^{-10} +z^2+2 a^{-2} -3 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +6 z^{10} a^{-6} +11 z^{10} a^{-8} +5 z^{10} a^{-10} +9 z^9 a^{-5} +9 z^9 a^{-7} +4 z^9 a^{-9} +4 z^9 a^{-11} +9 z^8 a^{-4} -6 z^8 a^{-6} -35 z^8 a^{-8} -19 z^8 a^{-10} +z^8 a^{-12} +8 z^7 a^{-3} -16 z^7 a^{-5} -46 z^7 a^{-7} -40 z^7 a^{-9} -18 z^7 a^{-11} +6 z^6 a^{-2} -11 z^6 a^{-4} -19 z^6 a^{-6} +19 z^6 a^{-8} +17 z^6 a^{-10} -4 z^6 a^{-12} +3 z^5 a^{-1} -9 z^5 a^{-3} +5 z^5 a^{-5} +46 z^5 a^{-7} +54 z^5 a^{-9} +25 z^5 a^{-11} -7 z^4 a^{-2} -z^4 a^{-4} +26 z^4 a^{-6} +16 z^4 a^{-8} +2 z^4 a^{-10} +5 z^4 a^{-12} +z^4-2 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -14 z^3 a^{-7} -18 z^3 a^{-9} -11 z^3 a^{-11} +6 z^2 a^{-2} +3 z^2 a^{-4} -15 z^2 a^{-6} -14 z^2 a^{-8} -5 z^2 a^{-10} -2 z^2 a^{-12} -z^2+z a^{-7} +z a^{-9} -2 a^{-2} +3 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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