K12n424
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+8 q^5-12 q^4+15 q^3-16 q^2+15 q-11+8 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-12 t^2+19 t-21+19 t^{-1} -12 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-2 z^4+1 }[/math] |
| Determinant | 95 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +z^6-8 z^4 a^{-2} +3 z^4 a^{-4} +3 z^4-4 z^2 a^{-2} +2 z^2 a^{-4} +2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +6 z^9 a^{-1} +9 z^9 a^{-3} +3 z^9 a^{-5} +4 z^8 a^{-2} -2 z^8 a^{-4} +z^8 a^{-6} +7 z^8+4 a z^7-16 z^7 a^{-1} -29 z^7 a^{-3} -9 z^7 a^{-5} +a^2 z^6-26 z^6 a^{-2} -2 z^6 a^{-4} +2 z^6 a^{-6} -21 z^6-10 a z^5+11 z^5 a^{-1} +37 z^5 a^{-3} +20 z^5 a^{-5} +4 z^5 a^{-7} -2 a^2 z^4+31 z^4 a^{-2} +11 z^4 a^{-4} -z^4 a^{-6} +z^4 a^{-8} +16 z^4+3 a z^3-4 z^3 a^{-1} -17 z^3 a^{-3} -15 z^3 a^{-5} -5 z^3 a^{-7} -10 z^2 a^{-2} -6 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} -5 z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} +z a^{-7} +1 }[/math] |
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