K12n498
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+7 q^5-10 q^4+13 q^3-13 q^2+12 q-9+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -5 t^2+20 t-29+20 t^{-1} -5 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-5 z^4 }[/math] |
| Determinant | 79 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -3 z^4 a^{-2} -z^4 a^{-4} -z^4+a^2 z^2-5 z^2 a^{-2} +2 z^2 a^{-4} +z^2 a^{-6} +z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +5 z^9 a^{-1} +8 z^9 a^{-3} +3 z^9 a^{-5} -z^8 a^{-2} -5 z^8 a^{-4} +z^8 a^{-6} +5 z^8+3 a z^7-18 z^7 a^{-1} -33 z^7 a^{-3} -12 z^7 a^{-5} +a^2 z^6-15 z^6 a^{-2} +4 z^6 a^{-4} +z^6 a^{-6} -17 z^6-9 a z^5+22 z^5 a^{-1} +54 z^5 a^{-3} +27 z^5 a^{-5} +4 z^5 a^{-7} -3 a^2 z^4+30 z^4 a^{-2} +9 z^4 a^{-4} -z^4 a^{-6} +z^4 a^{-8} +16 z^4+4 a z^3-13 z^3 a^{-1} -33 z^3 a^{-3} -22 z^3 a^{-5} -6 z^3 a^{-7} +a^2 z^2-18 z^2 a^{-2} -10 z^2 a^{-4} -2 z^2 a^{-6} -z^2 a^{-8} -8 z^2+3 z a^{-1} +7 z a^{-3} +5 z a^{-5} +z a^{-7} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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