K12a1234
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+5 q^7-10 q^6+14 q^5-18 q^4+20 q^3-19 q^2+16 q-11+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+7 t^3-15 t^2+25 t-29+25 t^{-1} -15 t^{-2} +7 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-9 z^6-13 z^4-4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -6 z^6 a^{-4} +z^6 a^{-6} +z^6-8 z^4 a^{-2} -14 z^4 a^{-4} +5 z^4 a^{-6} +4 z^4-3 z^2 a^{-2} -14 z^2 a^{-4} +8 z^2 a^{-6} +5 z^2+ a^{-2} -5 a^{-4} +3 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +5 z^9 a^{-1} +5 z^9 a^{-3} +4 z^9 a^{-5} +4 z^9 a^{-7} -2 z^8 a^{-2} -18 z^8 a^{-4} -8 z^8 a^{-6} +3 z^8 a^{-8} +5 z^8+3 a z^7-12 z^7 a^{-1} -18 z^7 a^{-3} -19 z^7 a^{-5} -14 z^7 a^{-7} +2 z^7 a^{-9} +a^2 z^6-8 z^6 a^{-2} +31 z^6 a^{-4} +15 z^6 a^{-6} -8 z^6 a^{-8} +z^6 a^{-10} -14 z^6-8 a z^5+10 z^5 a^{-1} +22 z^5 a^{-3} +37 z^5 a^{-5} +27 z^5 a^{-7} -6 z^5 a^{-9} -3 a^2 z^4+12 z^4 a^{-2} -30 z^4 a^{-4} -15 z^4 a^{-6} +7 z^4 a^{-8} -4 z^4 a^{-10} +13 z^4+4 a z^3-6 z^3 a^{-1} -7 z^3 a^{-3} -28 z^3 a^{-5} -27 z^3 a^{-7} +4 z^3 a^{-9} +2 a^2 z^2-4 z^2 a^{-2} +22 z^2 a^{-4} +7 z^2 a^{-6} -4 z^2 a^{-8} +4 z^2 a^{-10} -9 z^2+2 z a^{-3} +8 z a^{-5} +6 z a^{-7} - a^{-2} -5 a^{-4} -3 a^{-6} +2 }[/math] |
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