K13a3521
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Polynomial invariants
| Jones polynomial | Data:K13a3521/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+15 t^3-49 t^2+95 t-117+95 t^{-1} -49 t^{-2} +15 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a3521/Conway Polynomial |
| Determinant | 439 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4+3 z^4 a^{-2} -7 z^4 a^{-4} +2 z^4 a^{-6} +4 z^4-2 a^2 z^2+7 z^2 a^{-2} -9 z^2 a^{-4} +3 z^2 a^{-6} +3 z^2-a^2+4 a^{-2} -4 a^{-4} + a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{12} a^{-2} +4 z^{12} a^{-4} +11 z^{11} a^{-1} +27 z^{11} a^{-3} +16 z^{11} a^{-5} +30 z^{10} a^{-2} +44 z^{10} a^{-4} +27 z^{10} a^{-6} +13 z^{10}+9 a z^9-3 z^9 a^{-1} -29 z^9 a^{-3} +8 z^9 a^{-5} +25 z^9 a^{-7} +4 a^2 z^8-86 z^8 a^{-2} -115 z^8 a^{-4} -43 z^8 a^{-6} +14 z^8 a^{-8} -24 z^8+a^3 z^7-20 a z^7-33 z^7 a^{-1} -35 z^7 a^{-3} -74 z^7 a^{-5} -46 z^7 a^{-7} +5 z^7 a^{-9} -10 a^2 z^6+81 z^6 a^{-2} +100 z^6 a^{-4} +22 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +14 z^6-3 a^3 z^5+16 a z^5+42 z^5 a^{-1} +61 z^5 a^{-3} +82 z^5 a^{-5} +39 z^5 a^{-7} -5 z^5 a^{-9} +9 a^2 z^4-43 z^4 a^{-2} -50 z^4 a^{-4} -5 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} -2 z^4+3 a^3 z^3-5 a z^3-22 z^3 a^{-1} -37 z^3 a^{-3} -43 z^3 a^{-5} -19 z^3 a^{-7} +z^3 a^{-9} -4 a^2 z^2+16 z^2 a^{-2} +19 z^2 a^{-4} +2 z^2 a^{-6} -3 z^2 a^{-8} -2 z^2-a^3 z+5 z a^{-1} +11 z a^{-3} +10 z a^{-5} +3 z a^{-7} +a^2-4 a^{-2} -4 a^{-4} - a^{-6} +1 }[/math] |
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