K12a571
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-6 q^8+15 q^7-26 q^6+36 q^5-43 q^4+45 q^3-40 q^2+32 q-20+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+12 t^3-33 t^2+58 t-69+58 t^{-1} -33 t^{-2} +12 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-4 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 279 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -2 z^6 a^{-4} +z^6 a^{-6} +z^6-8 z^4 a^{-2} +3 z^4 a^{-4} +z^4 a^{-6} +3 z^4-8 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2-2 a^{-2} +4 a^{-4} -2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-3} +4 z^{11} a^{-5} +10 z^{10} a^{-2} +24 z^{10} a^{-4} +14 z^{10} a^{-6} +11 z^9 a^{-1} +21 z^9 a^{-3} +30 z^9 a^{-5} +20 z^9 a^{-7} -6 z^8 a^{-2} -35 z^8 a^{-4} -6 z^8 a^{-6} +15 z^8 a^{-8} +8 z^8+4 a z^7-16 z^7 a^{-1} -59 z^7 a^{-3} -79 z^7 a^{-5} -34 z^7 a^{-7} +6 z^7 a^{-9} +a^2 z^6-15 z^6 a^{-2} -4 z^6 a^{-4} -29 z^6 a^{-6} -24 z^6 a^{-8} +z^6 a^{-10} -14 z^6-8 a z^5+6 z^5 a^{-1} +50 z^5 a^{-3} +54 z^5 a^{-5} +12 z^5 a^{-7} -6 z^5 a^{-9} -2 a^2 z^4+27 z^4 a^{-2} +29 z^4 a^{-4} +20 z^4 a^{-6} +7 z^4 a^{-8} +9 z^4+5 a z^3+3 z^3 a^{-1} -10 z^3 a^{-3} -10 z^3 a^{-5} -2 z^3 a^{-7} +a^2 z^2-15 z^2 a^{-2} -17 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} -4 z^2-a z-2 z a^{-1} -z a^{-3} -z a^{-5} +z a^{-9} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1 }[/math] |
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