K12a1241
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-6 q^6+12 q^5-18 q^4+22 q^3-24 q^2+23 q-19+14 q^{-1} -8 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-18 t^2+35 t-41+35 t^{-1} -18 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+6 z^4-z^2+1 }[/math] |
| Determinant | 155 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+5 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} +z^4-a^2 z^2+3 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} -2 z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+6 a z^9+5 z^9 a^{-1} +7 z^9 a^{-3} +8 z^9 a^{-5} +4 a^2 z^8-36 z^8 a^{-2} -14 z^8 a^{-4} +7 z^8 a^{-6} -11 z^8+a^3 z^7-19 a z^7-31 z^7 a^{-1} -38 z^7 a^{-3} -22 z^7 a^{-5} +5 z^7 a^{-7} -14 a^2 z^6+49 z^6 a^{-2} +16 z^6 a^{-4} -15 z^6 a^{-6} +3 z^6 a^{-8} +z^6-3 a^3 z^5+15 a z^5+41 z^5 a^{-1} +64 z^5 a^{-3} +31 z^5 a^{-5} -9 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4-36 z^4 a^{-2} -4 z^4 a^{-4} +13 z^4 a^{-6} -6 z^4 a^{-8} +2 a^3 z^3-4 a z^3-29 z^3 a^{-1} -44 z^3 a^{-3} -15 z^3 a^{-5} +4 z^3 a^{-7} -2 z^3 a^{-9} -2 a^2 z^2+9 z^2 a^{-2} -z^2 a^{-6} +2 z^2 a^{-8} +4 z^2+2 a z+8 z a^{-1} +9 z a^{-3} +3 z a^{-5} -a^2- a^{-2} -1 }[/math] |
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