K12a213
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+21 q^5-30 q^4+37 q^3-39 q^2+36 q-29+20 q^{-1} -11 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+54 t-65+54 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^2+1 }[/math] |
| Determinant | 247 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +5 z^4-a^2 z^2-7 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +3 z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +16 z^{10} a^{-2} +9 z^{10} a^{-4} +7 z^{10}+9 a z^9+24 z^9 a^{-1} +32 z^9 a^{-3} +17 z^9 a^{-5} +5 a^2 z^8-9 z^8 a^{-2} +16 z^8 a^{-4} +18 z^8 a^{-6} -2 z^8+a^3 z^7-24 a z^7-75 z^7 a^{-1} -79 z^7 a^{-3} -17 z^7 a^{-5} +12 z^7 a^{-7} -14 a^2 z^6-56 z^6 a^{-2} -65 z^6 a^{-4} -25 z^6 a^{-6} +5 z^6 a^{-8} -35 z^6-2 a^3 z^5+19 a z^5+64 z^5 a^{-1} +54 z^5 a^{-3} -3 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4+67 z^4 a^{-2} +53 z^4 a^{-4} +13 z^4 a^{-6} -3 z^4 a^{-8} +42 z^4+a^3 z^3-4 a z^3-19 z^3 a^{-1} -14 z^3 a^{-3} +4 z^3 a^{-5} +4 z^3 a^{-7} -2 a^2 z^2-22 z^2 a^{-2} -15 z^2 a^{-4} -3 z^2 a^{-6} -12 z^2+2 z a^{-1} +2 z a^{-3} -a^2+ a^{-2} + a^{-4} }[/math] |
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