K12n819
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+12 q^5-16 q^4+18 q^3-17 q^2+15 q-10+6 q^{-1} -2 q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-12 t^2+24 t-29+24 t^{-1} -12 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +7 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} -2 z^4+8 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} -4 z^2+3 a^{-2} - a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +9 z^9 a^{-3} +6 z^9 a^{-5} -2 z^8 a^{-2} +5 z^8 a^{-4} +8 z^8 a^{-6} +z^8-7 z^7 a^{-1} -25 z^7 a^{-3} -12 z^7 a^{-5} +6 z^7 a^{-7} +8 z^6 a^{-2} -20 z^6 a^{-4} -21 z^6 a^{-6} +3 z^6 a^{-8} +4 z^6+3 a z^5+16 z^5 a^{-1} +37 z^5 a^{-3} +10 z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} -18 z^4 a^{-2} +25 z^4 a^{-4} +25 z^4 a^{-6} -5 z^4 a^{-8} -13 z^4-6 a z^3-24 z^3 a^{-1} -28 z^3 a^{-3} +2 z^3 a^{-5} +10 z^3 a^{-7} -2 z^3 a^{-9} +10 z^2 a^{-2} -8 z^2 a^{-4} -10 z^2 a^{-6} +8 z^2+3 a z+8 z a^{-1} +7 z a^{-3} -z a^{-5} -3 z a^{-7} -3 a^{-2} + a^{-6} -1 }[/math] |
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