K12a1198
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+18 q^5-26 q^4+33 q^3-35 q^2+33 q-27+19 q^{-1} -11 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+52 t-67+52 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+3 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +z^2 a^{-2} +2 z^2 a^{-4} -z^2 a^{-6} -2 z^2+a^2+2 a^{-4} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-1} +4 z^{11} a^{-3} +21 z^{10} a^{-2} +11 z^{10} a^{-4} +10 z^{10}+10 a z^9+9 z^9 a^{-1} +14 z^9 a^{-3} +15 z^9 a^{-5} +5 a^2 z^8-59 z^8 a^{-2} -14 z^8 a^{-4} +14 z^8 a^{-6} -26 z^8+a^3 z^7-31 a z^7-55 z^7 a^{-1} -60 z^7 a^{-3} -28 z^7 a^{-5} +9 z^7 a^{-7} -14 a^2 z^6+56 z^6 a^{-2} -3 z^6 a^{-4} -25 z^6 a^{-6} +4 z^6 a^{-8} +16 z^6-2 a^3 z^5+26 a z^5+63 z^5 a^{-1} +71 z^5 a^{-3} +23 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +8 a^2 z^4-22 z^4 a^{-2} +15 z^4 a^{-4} +20 z^4 a^{-6} -4 z^4 a^{-8} -5 z^4-6 a z^3-26 z^3 a^{-1} -34 z^3 a^{-3} -8 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} +a^2 z^2+2 z^2 a^{-2} -9 z^2 a^{-4} -7 z^2 a^{-6} +5 z^2+3 z a^{-1} +5 z a^{-3} +z a^{-5} -z a^{-7} -a^2+2 a^{-4} + a^{-6} -1 }[/math] |
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