K12a299
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-15 q^7+20 q^6-24 q^5+25 q^4-22 q^3+18 q^2-12 q+7-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+20 t^2-33 t+39-33 t^{-1} +20 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-2 z^4+1 }[/math] |
| Determinant | 161 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -8 z^4 a^{-2} +11 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-10 z^2 a^{-2} +13 z^2 a^{-4} -8 z^2 a^{-6} +2 z^2 a^{-8} +3 z^2-4 a^{-2} +6 a^{-4} -4 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +8 z^{10} a^{-4} +5 z^{10} a^{-6} +3 z^9 a^{-1} +9 z^9 a^{-3} +17 z^9 a^{-5} +11 z^9 a^{-7} -7 z^8 a^{-2} -13 z^8 a^{-4} +10 z^8 a^{-6} +15 z^8 a^{-8} +z^8-14 z^7 a^{-1} -47 z^7 a^{-3} -57 z^7 a^{-5} -10 z^7 a^{-7} +14 z^7 a^{-9} -9 z^6 a^{-2} -28 z^6 a^{-4} -56 z^6 a^{-6} -23 z^6 a^{-8} +9 z^6 a^{-10} -5 z^6+22 z^5 a^{-1} +63 z^5 a^{-3} +47 z^5 a^{-5} -17 z^5 a^{-7} -19 z^5 a^{-9} +4 z^5 a^{-11} +32 z^4 a^{-2} +59 z^4 a^{-4} +54 z^4 a^{-6} +10 z^4 a^{-8} -7 z^4 a^{-10} +z^4 a^{-12} +9 z^4-13 z^3 a^{-1} -28 z^3 a^{-3} -11 z^3 a^{-5} +15 z^3 a^{-7} +10 z^3 a^{-9} -z^3 a^{-11} -22 z^2 a^{-2} -31 z^2 a^{-4} -22 z^2 a^{-6} -4 z^2 a^{-8} +2 z^2 a^{-10} -7 z^2+2 z a^{-1} +4 z a^{-3} -4 z a^{-7} -2 z a^{-9} +4 a^{-2} +6 a^{-4} +4 a^{-6} + a^{-8} +2 }[/math] |
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