K12n800
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+9 q-14+18 q^{-1} -19 q^{-2} +19 q^{-3} -15 q^{-4} +10 q^{-5} -5 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-13 t^2+24 t-29+24 t^{-1} -13 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+a^4 z^6-5 a^2 z^6+z^6+3 a^4 z^4-9 a^2 z^4+3 z^4+4 a^4 z^2-6 a^2 z^2+3 z^2-a^6+2 a^4-a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^4 z^{10}+2 a^2 z^{10}+4 a^5 z^9+10 a^3 z^9+6 a z^9+2 a^6 z^8+4 a^4 z^8+9 a^2 z^8+7 z^8-8 a^5 z^7-20 a^3 z^7-8 a z^7+4 z^7 a^{-1} -15 a^4 z^6-32 a^2 z^6+z^6 a^{-2} -16 z^6+5 a^7 z^5+14 a^5 z^5+11 a^3 z^5-7 a z^5-9 z^5 a^{-1} +a^8 z^4+4 a^6 z^4+20 a^4 z^4+28 a^2 z^4-2 z^4 a^{-2} +9 z^4-4 a^7 z^3-5 a^5 z^3+a^3 z^3+7 a z^3+5 z^3 a^{-1} -a^8 z^2-4 a^6 z^2-9 a^4 z^2-11 a^2 z^2+z^2 a^{-2} -4 z^2-a^7 z-a^5 z-a^3 z-2 a z-z a^{-1} +a^6+2 a^4+a^2+1 }[/math] |
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