K13a1115
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Polynomial invariants
| Jones polynomial | Data:K13a1115/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+14 t^3-43 t^2+80 t-97+80 t^{-1} -43 t^{-2} +14 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1115/Conway Polynomial |
| Determinant | 375 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -2 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +2 z^6-a^2 z^4-z^4 a^{-2} -4 z^4 a^{-4} +2 z^4 a^{-6} +5 z^4-2 a^2 z^2-z^2 a^{-2} -z^2 a^{-4} +z^2 a^{-6} +5 z^2-a^2-2 a^{-2} +2 a^{-4} - a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12} a^{-4} +9 z^{11} a^{-1} +21 z^{11} a^{-3} +12 z^{11} a^{-5} +25 z^{10} a^{-2} +34 z^{10} a^{-4} +20 z^{10} a^{-6} +11 z^{10}+8 a z^9-5 z^9 a^{-1} -28 z^9 a^{-3} +4 z^9 a^{-5} +19 z^9 a^{-7} +4 a^2 z^8-85 z^8 a^{-2} -104 z^8 a^{-4} -33 z^8 a^{-6} +12 z^8 a^{-8} -22 z^8+a^3 z^7-18 a z^7-27 z^7 a^{-1} -29 z^7 a^{-3} -60 z^7 a^{-5} -34 z^7 a^{-7} +5 z^7 a^{-9} -11 a^2 z^6+99 z^6 a^{-2} +111 z^6 a^{-4} +14 z^6 a^{-6} -19 z^6 a^{-8} +z^6 a^{-10} +11 z^6-3 a^3 z^5+10 a z^5+40 z^5 a^{-1} +78 z^5 a^{-3} +78 z^5 a^{-5} +20 z^5 a^{-7} -7 z^5 a^{-9} +10 a^2 z^4-50 z^4 a^{-2} -45 z^4 a^{-4} +3 z^4 a^{-6} +8 z^4 a^{-8} -z^4 a^{-10} -z^4+3 a^3 z^3-a z^3-26 z^3 a^{-1} -49 z^3 a^{-3} -35 z^3 a^{-5} -6 z^3 a^{-7} +2 z^3 a^{-9} -4 a^2 z^2+4 z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} -2 z^2 a^{-8} -5 z^2-a^3 z+6 z a^{-1} +10 z a^{-3} +5 z a^{-5} +a^2+2 a^{-2} +2 a^{-4} + a^{-6} +3 }[/math] |
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