K12a224
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+19 q^5-27 q^4+34 q^3-37 q^2+34 q-28+20 q^{-1} -11 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-27 t^2+50 t-59+50 t^{-1} -27 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^4-2 z^2+1 }[/math] |
| Determinant | 231 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +5 z^4-a^2 z^2-9 z^2 a^{-2} +7 z^2 a^{-4} -2 z^2 a^{-6} +3 z^2+a^2-4 a^{-2} +4 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +8 z^{10} a^{-4} +7 z^{10}+9 a z^9+22 z^9 a^{-1} +27 z^9 a^{-3} +14 z^9 a^{-5} +5 a^2 z^8-11 z^8 a^{-2} +11 z^8 a^{-4} +14 z^8 a^{-6} -3 z^8+a^3 z^7-24 a z^7-71 z^7 a^{-1} -72 z^7 a^{-3} -17 z^7 a^{-5} +9 z^7 a^{-7} -14 a^2 z^6-50 z^6 a^{-2} -56 z^6 a^{-4} -22 z^6 a^{-6} +4 z^6 a^{-8} -34 z^6-2 a^3 z^5+18 a z^5+62 z^5 a^{-1} +59 z^5 a^{-3} +5 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4+69 z^4 a^{-2} +62 z^4 a^{-4} +19 z^4 a^{-6} -4 z^4 a^{-8} +42 z^4+a^3 z^3-4 a z^3-24 z^3 a^{-1} -24 z^3 a^{-3} +2 z^3 a^{-5} +6 z^3 a^{-7} -z^3 a^{-9} -2 a^2 z^2-32 z^2 a^{-2} -29 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} -14 z^2+a z+6 z a^{-1} +6 z a^{-3} -z a^{-7} -a^2+4 a^{-2} +4 a^{-4} + a^{-6} +1 }[/math] |
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