# 10 96 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 96's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 96 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X5,18,6,19 X3948 X9,3,10,2 X11,17,12,16 X7,12,8,13 X15,6,16,7 X17,11,18,10 X13,1,14,20 X19,15,20,14 Gauss code -1, 4, -3, 1, -2, 7, -6, 3, -4, 8, -5, 6, -9, 10, -7, 5, -8, 2, -10, 9 Dowker-Thistlethwaite code 4 8 18 12 2 16 20 6 10 14 Conway Notation [.2.21.2]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-5][-7] Hyperbolic Volume 15.1779 A-Polynomial See Data:10 96/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-t^3+7 t^2-22 t+33-22 t^{-1} +7 t^{-2} - t^{-3}$ Conway polynomial $-z^6+z^4-3 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 93, 0 } Jones polynomial $q^6-3 q^5+7 q^4-11 q^3+14 q^2-16 q+15-12 q^{-1} +9 q^{-2} -4 q^{-3} + q^{-4}$ HOMFLY-PT polynomial (db, data sources) $-z^6+a^2 z^4+3 z^4 a^{-2} -3 z^4+a^2 z^2+5 z^2 a^{-2} -3 z^2 a^{-4} -6 z^2+2 a^2+3 a^{-2} -2 a^{-4} + a^{-6} -3$ Kauffman polynomial (db, data sources) $2 z^9 a^{-1} +2 z^9 a^{-3} +11 z^8 a^{-2} +4 z^8 a^{-4} +7 z^8+11 a z^7+14 z^7 a^{-1} +6 z^7 a^{-3} +3 z^7 a^{-5} +9 a^2 z^6-17 z^6 a^{-2} -7 z^6 a^{-4} +z^6 a^{-6} +4 a^3 z^5-15 a z^5-34 z^5 a^{-1} -23 z^5 a^{-3} -8 z^5 a^{-5} +a^4 z^4-10 a^2 z^4-4 z^4 a^{-2} -z^4 a^{-4} -3 z^4 a^{-6} -17 z^4-a^3 z^3+7 a z^3+17 z^3 a^{-1} +16 z^3 a^{-3} +7 z^3 a^{-5} +5 a^2 z^2+10 z^2 a^{-2} +6 z^2 a^{-4} +3 z^2 a^{-6} +12 z^2-a z-z a^{-1} -2 z a^{-3} -2 z a^{-5} -2 a^2-3 a^{-2} -2 a^{-4} - a^{-6} -3$ The A2 invariant $q^{12}-2 q^{10}+3 q^8+2 q^6-3 q^4+3 q^2-3+ q^{-2} - q^{-6} +3 q^{-8} -3 q^{-10} + q^{-12} + q^{-14} -2 q^{-16} + q^{-18} + q^{-20}$ The G2 invariant $q^{66}-3 q^{64}+6 q^{62}-10 q^{60}+11 q^{58}-10 q^{56}+4 q^{54}+15 q^{52}-37 q^{50}+63 q^{48}-80 q^{46}+68 q^{44}-36 q^{42}-30 q^{40}+119 q^{38}-191 q^{36}+229 q^{34}-189 q^{32}+78 q^{30}+83 q^{28}-238 q^{26}+334 q^{24}-324 q^{22}+195 q^{20}+4 q^{18}-197 q^{16}+307 q^{14}-272 q^{12}+120 q^{10}+86 q^8-245 q^6+269 q^4-161 q^2-63+294 q^{-2} -425 q^{-4} +394 q^{-6} -202 q^{-8} -84 q^{-10} +357 q^{-12} -513 q^{-14} +493 q^{-16} -322 q^{-18} +52 q^{-20} +219 q^{-22} -388 q^{-24} +414 q^{-26} -276 q^{-28} +57 q^{-30} +160 q^{-32} -281 q^{-34} +251 q^{-36} -98 q^{-38} -109 q^{-40} +278 q^{-42} -326 q^{-44} +228 q^{-46} -21 q^{-48} -206 q^{-50} +357 q^{-52} -373 q^{-54} +255 q^{-56} -70 q^{-58} -122 q^{-60} +239 q^{-62} -260 q^{-64} +201 q^{-66} -91 q^{-68} -11 q^{-70} +76 q^{-72} -97 q^{-74} +81 q^{-76} -47 q^{-78} +18 q^{-80} +4 q^{-82} -13 q^{-84} +13 q^{-86} -10 q^{-88} +6 q^{-90} -2 q^{-92} + q^{-94}$