K12a1253
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-10 q^2+17 q-24+31 q^{-1} -32 q^{-2} +31 q^{-3} -25 q^{-4} +17 q^{-5} -10 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-5 t^4+14 t^3-26 t^2+37 t-41+37 t^{-1} -26 t^{-2} +14 t^{-3} -5 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+5 z^8+9 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 207 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+7 a^2 z^8-z^8-5 a^4 z^6+19 a^2 z^6-5 z^6-9 a^4 z^4+26 a^2 z^4-9 z^4-8 a^4 z^2+20 a^2 z^2-8 z^2-4 a^4+8 a^2-3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+9 a^4 z^{10}+16 a^2 z^{10}+7 z^{10}+13 a^5 z^9+13 a^3 z^9+7 a z^9+7 z^9 a^{-1} +13 a^6 z^8-9 a^4 z^8-41 a^2 z^8+4 z^8 a^{-2} -15 z^8+9 a^7 z^7-21 a^5 z^7-45 a^3 z^7-35 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-22 a^6 z^6-a^4 z^6+43 a^2 z^6-12 z^6 a^{-2} +6 z^6+a^9 z^5-13 a^7 z^5+14 a^5 z^5+49 a^3 z^5+36 a z^5+12 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+16 a^6 z^4-a^4 z^4-36 a^2 z^4+10 z^4 a^{-2} -5 z^4-a^9 z^3+7 a^7 z^3-4 a^5 z^3-29 a^3 z^3-21 a z^3-z^3 a^{-1} +3 z^3 a^{-3} -4 a^6 z^2+8 a^4 z^2+22 a^2 z^2-2 z^2 a^{-2} +8 z^2-2 a^7 z+2 a^5 z+9 a^3 z+7 a z+z a^{-1} -z a^{-3} -4 a^4-8 a^2-3 }[/math] |
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