K12a138
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+20 q^5-28 q^4+34 q^3-35 q^2+32 q-25+17 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-26 t^2+48 t-57+48 t^{-1} -26 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+2 z^4+1 }[/math] |
| Determinant | 223 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +5 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +14 z^{10} a^{-2} +8 z^{10} a^{-4} +6 z^{10}+7 a z^9+16 z^9 a^{-1} +24 z^9 a^{-3} +15 z^9 a^{-5} +4 a^2 z^8-17 z^8 a^{-2} +11 z^8 a^{-4} +17 z^8 a^{-6} -7 z^8+a^3 z^7-21 a z^7-58 z^7 a^{-1} -62 z^7 a^{-3} -14 z^7 a^{-5} +12 z^7 a^{-7} -13 a^2 z^6-23 z^6 a^{-2} -48 z^6 a^{-4} -24 z^6 a^{-6} +5 z^6 a^{-8} -17 z^6-3 a^3 z^5+20 a z^5+60 z^5 a^{-1} +47 z^5 a^{-3} -5 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +13 a^2 z^4+38 z^4 a^{-2} +36 z^4 a^{-4} +11 z^4 a^{-6} -3 z^4 a^{-8} +29 z^4+2 a^3 z^3-8 a z^3-23 z^3 a^{-1} -15 z^3 a^{-3} +2 z^3 a^{-5} +4 z^3 a^{-7} -5 a^2 z^2-12 z^2 a^{-2} -8 z^2 a^{-4} -3 z^2 a^{-6} -12 z^2+a z+3 z a^{-1} +3 z a^{-3} +z a^{-5} +1 }[/math] |
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