K13a636
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Polynomial invariants
| Jones polynomial | Data:K13a636/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-12 t^3+20 t^2-25 t+27-25 t^{-1} +20 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13a636/Conway Polynomial |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^{10}+a^6 z^8-8 a^4 z^8+2 a^2 z^8+6 a^6 z^6-26 a^4 z^6+14 a^2 z^6-z^6+13 a^6 z^4-45 a^4 z^4+36 a^2 z^4-6 z^4+13 a^6 z^2-42 a^4 z^2+42 a^2 z^2-11 z^2+5 a^6-17 a^4+19 a^2-6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-2 z^3 a^{11}+6 z^6 a^{10}-6 z^4 a^{10}+3 z^2 a^{10}+9 z^7 a^9-14 z^5 a^9+11 z^3 a^9-3 z a^9+10 z^8 a^8-17 z^6 a^8+8 z^4 a^8+10 z^9 a^7-23 z^7 a^7+18 z^5 a^7-10 z^3 a^7+2 z a^7+8 z^{10} a^6-21 z^8 a^6+17 z^6 a^6-14 z^4 a^6+10 z^2 a^6-5 a^6+4 z^{11} a^5-3 z^9 a^5-32 z^7 a^5+67 z^5 a^5-61 z^3 a^5+22 z a^5+z^{12} a^4+8 z^{10} a^4-49 z^8 a^4+83 z^6 a^4-77 z^4 a^4+50 z^2 a^4-17 a^4+6 z^{11} a^3-21 z^9 a^3+2 z^7 a^3+55 z^5 a^3-69 z^3 a^3+30 z a^3+z^{12} a^2+2 z^{10} a^2-30 z^8 a^2+68 z^6 a^2-73 z^4 a^2+52 z^2 a^2-19 a^2+2 z^{11} a-7 z^9 a-5 z^7 a+40 z^5 a-48 z^3 a+19 z a+2 z^{10}-12 z^8+25 z^6-25 z^4+16 z^2-6+z^9 a^{-1} -7 z^7 a^{-1} +17 z^5 a^{-1} -17 z^3 a^{-1} +6 z a^{-1} }[/math] |
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