K12a614
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+12 q^7-20 q^6+28 q^5-33 q^4+34 q^3-31 q^2+24 q-15+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-20 t^2+51 t-67+51 t^{-1} -20 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-2 z^4-2 z^2+1 }[/math] |
| Determinant | 215 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +4 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-3 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +5 z^{10} a^{-2} +13 z^{10} a^{-4} +8 z^{10} a^{-6} +6 z^9 a^{-1} +13 z^9 a^{-3} +20 z^9 a^{-5} +13 z^9 a^{-7} +z^8 a^{-2} -15 z^8 a^{-4} +11 z^8 a^{-8} +5 z^8+3 a z^7-6 z^7 a^{-1} -32 z^7 a^{-3} -52 z^7 a^{-5} -24 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-14 z^6 a^{-2} -10 z^6 a^{-4} -28 z^6 a^{-6} -22 z^6 a^{-8} +z^6 a^{-10} -8 z^6-7 a z^5-2 z^5 a^{-1} +27 z^5 a^{-3} +40 z^5 a^{-5} +10 z^5 a^{-7} -8 z^5 a^{-9} -3 a^2 z^4+17 z^4 a^{-2} +24 z^4 a^{-4} +24 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +2 z^4+5 a z^3+3 z^3 a^{-1} -6 z^3 a^{-3} -8 z^3 a^{-5} -2 z^3 a^{-7} +2 z^3 a^{-9} +3 a^2 z^2-9 z^2 a^{-2} -10 z^2 a^{-4} -5 z^2 a^{-6} -2 z^2 a^{-8} +z^2-a z-z a^{-1} -z a^{-3} -z a^{-5} -a^2+ a^{-2} + a^{-4} }[/math] |
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