K12a1201
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+17 q^4-25 q^3+32 q^2-33 q+32-26 q^{-1} +18 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-43 t+51-43 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +4 z^6-3 a^2 z^4+6 z^4 a^{-2} -3 z^4 a^{-4} +6 z^4-3 a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} +4 z^2-a^2+3 a^{-2} -2 a^{-4} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +17 z^{10} a^{-2} +8 z^{10} a^{-4} +9 z^{10}+14 a z^9+16 z^9 a^{-1} +10 z^9 a^{-3} +8 z^9 a^{-5} +14 a^2 z^8-42 z^8 a^{-2} -21 z^8 a^{-4} +4 z^8 a^{-6} -3 z^8+9 a^3 z^7-22 a z^7-54 z^7 a^{-1} -50 z^7 a^{-3} -26 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-25 a^2 z^6+35 z^6 a^{-2} +18 z^6 a^{-4} -12 z^6 a^{-6} -24 z^6+a^5 z^5-12 a^3 z^5+10 a z^5+54 z^5 a^{-1} +62 z^5 a^{-3} +28 z^5 a^{-5} -3 z^5 a^{-7} -4 a^4 z^4+21 a^2 z^4-16 z^4 a^{-2} -12 z^4 a^{-4} +9 z^4 a^{-6} +30 z^4-a^5 z^3+6 a^3 z^3+4 a z^3-23 z^3 a^{-1} -37 z^3 a^{-3} -15 z^3 a^{-5} +2 z^3 a^{-7} -8 a^2 z^2+5 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} -10 z^2-2 a^3 z-2 a z+4 z a^{-1} +9 z a^{-3} +5 z a^{-5} +a^2-3 a^{-2} -2 a^{-4} +1 }[/math] |
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