K12a498
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-11 q^6+18 q^5-26 q^4+31 q^3-32 q^2+30 q-23+16 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-23 t^2+45 t-55+45 t^{-1} -23 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-z^4+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-12 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +7 z^4-2 a^2 z^2-12 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +9 z^2-a^2-3 a^{-2} + a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +9 z^{10} a^{-2} +5 z^{10} a^{-4} +4 z^{10}+6 a z^9+17 z^9 a^{-1} +22 z^9 a^{-3} +11 z^9 a^{-5} +4 a^2 z^8+6 z^8 a^{-2} +20 z^8 a^{-4} +14 z^8 a^{-6} +4 z^8+a^3 z^7-15 a z^7-46 z^7 a^{-1} -42 z^7 a^{-3} -z^7 a^{-5} +11 z^7 a^{-7} -13 a^2 z^6-63 z^6 a^{-2} -59 z^6 a^{-4} -17 z^6 a^{-6} +5 z^6 a^{-8} -39 z^6-3 a^3 z^5+7 a z^5+27 z^5 a^{-1} +8 z^5 a^{-3} -24 z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+71 z^4 a^{-2} +45 z^4 a^{-4} +5 z^4 a^{-6} -4 z^4 a^{-8} +49 z^4+3 a^3 z^3+5 a z^3+5 z^3 a^{-1} +15 z^3 a^{-3} +17 z^3 a^{-5} +5 z^3 a^{-7} -6 a^2 z^2-28 z^2 a^{-2} -13 z^2 a^{-4} -z^2 a^{-6} -22 z^2-a^3 z-3 a z-5 z a^{-1} -5 z a^{-3} -2 z a^{-5} +a^2+3 a^{-2} + a^{-4} +4 }[/math] |
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