K12a998
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+10 q^7-19 q^6+29 q^5-37 q^4+40 q^3-38 q^2+32 q-22+13 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-30 t^2+52 t-61+52 t^{-1} -30 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-4 z^4-z^2+1 }[/math] |
| Determinant | 251 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -3 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-2 z^4 a^{-2} -7 z^4 a^{-4} +3 z^4 a^{-6} +2 z^4+z^2 a^{-2} -6 z^2 a^{-4} +3 z^2 a^{-6} +z^2+ a^{-2} -2 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +12 z^{10} a^{-2} +22 z^{10} a^{-4} +10 z^{10} a^{-6} +16 z^9 a^{-1} +19 z^9 a^{-3} +14 z^9 a^{-5} +11 z^9 a^{-7} -13 z^8 a^{-2} -48 z^8 a^{-4} -15 z^8 a^{-6} +8 z^8 a^{-8} +12 z^8+5 a z^7-32 z^7 a^{-1} -60 z^7 a^{-3} -48 z^7 a^{-5} -21 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-7 z^6 a^{-2} +45 z^6 a^{-4} +12 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -23 z^6-7 a z^5+20 z^5 a^{-1} +57 z^5 a^{-3} +56 z^5 a^{-5} +18 z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+7 z^4 a^{-2} -25 z^4 a^{-4} -9 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} +12 z^4+a z^3-7 z^3 a^{-1} -23 z^3 a^{-3} -30 z^3 a^{-5} -11 z^3 a^{-7} +4 z^3 a^{-9} +z^2 a^{-2} +10 z^2 a^{-4} +4 z^2 a^{-6} -z^2 a^{-8} +z^2 a^{-10} -3 z^2+z a^{-1} +4 z a^{-3} +6 z a^{-5} +3 z a^{-7} - a^{-2} -2 a^{-4} - a^{-6} +1 }[/math] |
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