K12a1114
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -5 q^{-2} +8 q^{-3} -10 q^{-4} +13 q^{-5} -13 q^{-6} +13 q^{-7} -11 q^{-8} +8 q^{-9} -6 q^{-10} +3 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+9 t^3-12 t^2+14 t-15+14 t^{-1} -12 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+12 z^6+12 z^4+8 z^2+1 }[/math] |
| Determinant | 95 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+8 a^6 z^8-a^4 z^8-6 a^8 z^6+24 a^6 z^6-6 a^4 z^6-12 a^8 z^4+35 a^6 z^4-11 a^4 z^4-11 a^8 z^2+26 a^6 z^2-7 a^4 z^2-5 a^8+8 a^6-2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}+3 z^4 a^{14}+6 z^5 a^{13}-5 z^3 a^{13}+2 z a^{13}+8 z^6 a^{12}-10 z^4 a^{12}+2 z^2 a^{12}+9 z^7 a^{11}-16 z^5 a^{11}+4 z^3 a^{11}-2 z a^{11}+9 z^8 a^{10}-22 z^6 a^{10}+10 z^4 a^{10}-3 z^2 a^{10}+8 z^9 a^9-25 z^7 a^9+17 z^5 a^9-4 z^3 a^9+z a^9+6 z^{10} a^8-23 z^8 a^8+25 z^6 a^8-19 z^4 a^8+18 z^2 a^8-5 a^8+2 z^{11} a^7-35 z^7 a^7+70 z^5 a^7-44 z^3 a^7+11 z a^7+9 z^{10} a^6-51 z^8 a^6+95 z^6 a^6-75 z^4 a^6+33 z^2 a^6-8 a^6+2 z^{11} a^5-7 z^9 a^5-7 z^7 a^5+43 z^5 a^5-40 z^3 a^5+9 z a^5+3 z^{10} a^4-19 z^8 a^4+40 z^6 a^4-33 z^4 a^4+10 z^2 a^4-2 a^4+z^9 a^3-6 z^7 a^3+12 z^5 a^3-10 z^3 a^3+3 z a^3 }[/math] |
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