K12a1251
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-22 q^3+32 q^2-39 q+43-39 q^{-1} +32 q^{-2} -22 q^{-3} +12 q^{-4} -5 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+25 t^2-62 t+83-62 t^{-1} +25 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6+z^4+2 z^2+1 }[/math] |
| Determinant | 265 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4+z^4 a^{-4} -z^4-a^2 z^2-z^2 a^{-2} +4 z^2-2 a^2-2 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a z^{11}+5 z^{11} a^{-1} +13 a^2 z^{10}+13 z^{10} a^{-2} +26 z^{10}+15 a^3 z^9+16 a z^9+16 z^9 a^{-1} +15 z^9 a^{-3} +11 a^4 z^8-19 a^2 z^8-19 z^8 a^{-2} +11 z^8 a^{-4} -60 z^8+5 a^5 z^7-28 a^3 z^7-58 a z^7-58 z^7 a^{-1} -28 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-20 a^4 z^6+3 a^2 z^6+3 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +48 z^6-8 a^5 z^5+13 a^3 z^5+54 a z^5+54 z^5 a^{-1} +13 z^5 a^{-3} -8 z^5 a^{-5} -a^6 z^4+8 a^4 z^4+7 a^2 z^4+7 z^4 a^{-2} +8 z^4 a^{-4} -z^4 a^{-6} -4 z^4+2 a^5 z^3-10 a z^3-10 z^3 a^{-1} +2 z^3 a^{-5} -a^4 z^2-6 a^2 z^2-6 z^2 a^{-2} -z^2 a^{-4} -10 z^2-2 a^3 z-4 a z-4 z a^{-1} -2 z a^{-3} +2 a^2+2 a^{-2} +5 }[/math] |
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