K12a932
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+10 q^5-18 q^4+26 q^3-31 q^2+33 q-31+25 q^{-1} -17 q^{-2} +10 q^{-3} -4 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+46 t-55+46 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4-3 z^2+1 }[/math] |
| Determinant | 211 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +3 z^6-3 a^2 z^4-12 z^4 a^{-2} +3 z^4 a^{-4} +10 z^4+a^4 z^2-6 a^2 z^2-13 z^2 a^{-2} +4 z^2 a^{-4} +11 z^2+a^4-2 a^2-4 a^{-2} +2 a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +6 a^2 z^{10}+12 z^{10} a^{-2} +18 z^{10}+4 a^3 z^9+7 a z^9+25 z^9 a^{-1} +22 z^9 a^{-3} +a^4 z^8-19 a^2 z^8-4 z^8 a^{-2} +24 z^8 a^{-4} -48 z^8-16 a^3 z^7-57 a z^7-102 z^7 a^{-1} -43 z^7 a^{-3} +18 z^7 a^{-5} -4 a^4 z^6+11 a^2 z^6-60 z^6 a^{-2} -45 z^6 a^{-4} +10 z^6 a^{-6} +10 z^6+22 a^3 z^5+79 a z^5+102 z^5 a^{-1} +18 z^5 a^{-3} -23 z^5 a^{-5} +4 z^5 a^{-7} +6 a^4 z^4+13 a^2 z^4+70 z^4 a^{-2} +28 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +42 z^4-12 a^3 z^3-34 a z^3-36 z^3 a^{-1} -4 z^3 a^{-3} +10 z^3 a^{-5} -4 a^4 z^2-12 a^2 z^2-29 z^2 a^{-2} -10 z^2 a^{-4} +2 z^2 a^{-6} -25 z^2+2 a^3 z+4 a z+4 z a^{-1} +z a^{-3} -z a^{-5} +a^4+2 a^2+4 a^{-2} +2 a^{-4} +4 }[/math] |
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