K12a312
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{11}-4 q^{10}+8 q^9-14 q^8+19 q^7-23 q^6+25 q^5-22 q^4+19 q^3-13 q^2+7 q-3+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -9 t^2+40 t-61+40 t^{-1} -9 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -9 z^4+4 z^2+1 }[/math] |
| Determinant | 159 |
| 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} -4 z^2 a^{-6} +3 z^2 a^{-8} +z^2 a^{-10} +z^2+3 a^{-4} -3 a^{-6} +2 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +7 z^{10} a^{-6} +12 z^{10} a^{-8} +5 z^{10} a^{-10} +12 z^9 a^{-5} +14 z^9 a^{-7} +6 z^9 a^{-9} +4 z^9 a^{-11} +13 z^8 a^{-4} -4 z^8 a^{-6} -36 z^8 a^{-8} -18 z^8 a^{-10} +z^8 a^{-12} +10 z^7 a^{-3} -26 z^7 a^{-5} -67 z^7 a^{-7} -49 z^7 a^{-9} -18 z^7 a^{-11} +6 z^6 a^{-2} -28 z^6 a^{-4} -37 z^6 a^{-6} +15 z^6 a^{-8} +14 z^6 a^{-10} -4 z^6 a^{-12} +3 z^5 a^{-1} -15 z^5 a^{-3} +17 z^5 a^{-5} +82 z^5 a^{-7} +73 z^5 a^{-9} +26 z^5 a^{-11} -5 z^4 a^{-2} +27 z^4 a^{-4} +55 z^4 a^{-6} +22 z^4 a^{-8} +5 z^4 a^{-10} +5 z^4 a^{-12} +z^4-2 z^3 a^{-1} +10 z^3 a^{-3} -8 z^3 a^{-5} -46 z^3 a^{-7} -39 z^3 a^{-9} -13 z^3 a^{-11} +2 z^2 a^{-2} -14 z^2 a^{-4} -30 z^2 a^{-6} -16 z^2 a^{-8} -5 z^2 a^{-10} -2 z^2 a^{-12} -z^2+3 z a^{-5} +11 z a^{-7} +9 z a^{-9} +z a^{-11} +3 a^{-4} +3 a^{-6} +2 a^{-8} + a^{-10} }[/math] |
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