K12a695
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-22 q^6+33 q^5-41 q^4+44 q^3-41 q^2+34 q-23+13 q^{-1} -5 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+61 t-77+61 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+z^2+1 }[/math] |
| Determinant | 275 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-8 z^4 a^{-2} +8 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-6 z^2 a^{-2} +8 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +2 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +11 z^{10} a^{-2} +21 z^{10} a^{-4} +10 z^{10} a^{-6} +16 z^9 a^{-1} +32 z^9 a^{-3} +30 z^9 a^{-5} +14 z^9 a^{-7} +2 z^8 a^{-2} -17 z^8 a^{-4} +4 z^8 a^{-6} +11 z^8 a^{-8} +12 z^8+5 a z^7-28 z^7 a^{-1} -84 z^7 a^{-3} -77 z^7 a^{-5} -21 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-43 z^6 a^{-2} -42 z^6 a^{-4} -43 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} -22 z^6-7 a z^5+16 z^5 a^{-1} +68 z^5 a^{-3} +59 z^5 a^{-5} +6 z^5 a^{-7} -8 z^5 a^{-9} -a^2 z^4+44 z^4 a^{-2} +59 z^4 a^{-4} +43 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +14 z^4+2 a z^3-6 z^3 a^{-1} -21 z^3 a^{-3} -14 z^3 a^{-5} +2 z^3 a^{-7} +3 z^3 a^{-9} -16 z^2 a^{-2} -22 z^2 a^{-4} -14 z^2 a^{-6} -3 z^2 a^{-8} -5 z^2+z a^{-1} +2 z a^{-3} -z a^{-7} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
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