K12n226
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-4 q^7+7 q^6-10 q^5+12 q^4-12 q^3+12 q^2-9 q+6-3 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+11 t^2-14 t+15-14 t^{-1} +11 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+z^4+z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -9 z^4 a^{-2} +14 z^4 a^{-4} -5 z^4 a^{-6} +z^4-12 z^2 a^{-2} +17 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} +3 z^2-5 a^{-2} +8 a^{-4} -5 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +10 z^9 a^{-3} +7 z^9 a^{-5} -3 z^8 a^{-2} +6 z^8 a^{-4} +10 z^8 a^{-6} +z^8-15 z^7 a^{-1} -43 z^7 a^{-3} -21 z^7 a^{-5} +7 z^7 a^{-7} -18 z^6 a^{-2} -52 z^6 a^{-4} -37 z^6 a^{-6} +2 z^6 a^{-8} -5 z^6+24 z^5 a^{-1} +51 z^5 a^{-3} +6 z^5 a^{-5} -21 z^5 a^{-7} +42 z^4 a^{-2} +75 z^4 a^{-4} +42 z^4 a^{-6} +9 z^4-13 z^3 a^{-1} -17 z^3 a^{-3} +12 z^3 a^{-5} +20 z^3 a^{-7} +4 z^3 a^{-9} -27 z^2 a^{-2} -39 z^2 a^{-4} -22 z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -7 z^2+z a^{-1} -6 z a^{-5} -7 z a^{-7} -2 z a^{-9} +5 a^{-2} +8 a^{-4} +5 a^{-6} + a^{-8} +2 }[/math] |
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