# 8 13 (KnotPlot image) See the full Rolfsen Knot Table. Visit 8 13's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 8 13 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3,10,4,11 X11,1,12,16 X5,13,6,12 X15,7,16,6 X7,15,8,14 X13,9,14,8 X9,2,10,3 Gauss code -1, 8, -2, 1, -4, 5, -6, 7, -8, 2, -3, 4, -7, 6, -5, 3 Dowker-Thistlethwaite code 4 10 12 14 2 16 8 6 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 2 Bridge index 2 Super bridge index $\{4,5\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-4][-6] Hyperbolic Volume 8.53123 A-Polynomial See Data:8 13/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $2$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $2 t^2-7 t+11-7 t^{-1} +2 t^{-2}$ Conway polynomial $2 z^4+z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 29, 0 } Jones polynomial $-q^5+2 q^4-3 q^3+5 q^2-5 q+5-4 q^{-1} +3 q^{-2} - q^{-3}$ HOMFLY-PT polynomial (db, data sources) $z^4 a^{-2} +z^4-a^2 z^2+2 z^2 a^{-2} -z^2 a^{-4} +z^2+2 a^{-2} - a^{-4}$ Kauffman polynomial (db, data sources) $z^7 a^{-1} +z^7 a^{-3} +5 z^6 a^{-2} +2 z^6 a^{-4} +3 z^6+4 a z^5+4 z^5 a^{-1} +z^5 a^{-3} +z^5 a^{-5} +3 a^2 z^4-11 z^4 a^{-2} -6 z^4 a^{-4} -2 z^4+a^3 z^3-4 a z^3-9 z^3 a^{-1} -7 z^3 a^{-3} -3 z^3 a^{-5} -2 a^2 z^2+7 z^2 a^{-2} +5 z^2 a^{-4} +a z+3 z a^{-1} +4 z a^{-3} +2 z a^{-5} -2 a^{-2} - a^{-4}$ The A2 invariant $-q^{10}+q^8+q^6-q^4+q^2-1+ q^{-2} + q^{-4} + q^{-6} +2 q^{-8} - q^{-10} - q^{-16}$ The G2 invariant $q^{52}-2 q^{50}+3 q^{48}-4 q^{46}+q^{44}-3 q^{40}+9 q^{38}-11 q^{36}+12 q^{34}-8 q^{32}+6 q^{28}-13 q^{26}+18 q^{24}-16 q^{22}+10 q^{20}-8 q^{16}+14 q^{14}-10 q^{12}+4 q^{10}+2 q^8-10 q^6+9 q^4-3 q^2-7+17 q^{-2} -22 q^{-4} +19 q^{-6} -6 q^{-8} -9 q^{-10} +19 q^{-12} -26 q^{-14} +26 q^{-16} -14 q^{-18} +3 q^{-20} +11 q^{-22} -16 q^{-24} +21 q^{-26} -10 q^{-28} + q^{-30} +6 q^{-32} -9 q^{-34} +8 q^{-36} -6 q^{-40} +14 q^{-42} -15 q^{-44} +9 q^{-46} + q^{-48} -13 q^{-50} +18 q^{-52} -19 q^{-54} +11 q^{-56} -4 q^{-58} -6 q^{-60} +11 q^{-62} -13 q^{-64} +10 q^{-66} -4 q^{-68} - q^{-70} +2 q^{-72} -4 q^{-74} +3 q^{-76} - q^{-78} + q^{-80}$