# 10 48 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 48's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 48 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X8493 X14,6,15,5 X20,15,1,16 X16,9,17,10 X18,11,19,12 X10,17,11,18 X12,19,13,20 X2837 X4,14,5,13 Gauss code 1, -9, 2, -10, 3, -1, 9, -2, 5, -7, 6, -8, 10, -3, 4, -5, 7, -6, 8, -4 Dowker-Thistlethwaite code 6 8 14 2 16 18 4 20 10 12 Conway Notation [41,3,2]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 4 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-6] Hyperbolic Volume 10.3789 A-Polynomial See Data:10 48/A-polynomial

### Four dimensional invariants

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

### Polynomial invariants

 Alexander polynomial $t^4-3 t^3+6 t^2-9 t+11-9 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4}$ Conway polynomial $z^8+5 z^6+8 z^4+4 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 49, 0 } Jones polynomial $-q^5+2 q^4-4 q^3+6 q^2-7 q+9-7 q^{-1} +6 q^{-2} -4 q^{-3} +2 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $z^8-a^2 z^6-z^6 a^{-2} +7 z^6-5 a^2 z^4-5 z^4 a^{-2} +18 z^4-8 a^2 z^2-8 z^2 a^{-2} +20 z^2-4 a^2-4 a^{-2} +9$ Kauffman polynomial (db, data sources) $a z^9+z^9 a^{-1} +2 a^2 z^8+3 z^8 a^{-2} +5 z^8+2 a^3 z^7+z^7 a^{-1} +3 z^7 a^{-3} +2 a^4 z^6-5 a^2 z^6-11 z^6 a^{-2} +2 z^6 a^{-4} -20 z^6+a^5 z^5-3 a^3 z^5-5 a z^5-11 z^5 a^{-1} -9 z^5 a^{-3} +z^5 a^{-5} -5 a^4 z^4+9 a^2 z^4+18 z^4 a^{-2} -5 z^4 a^{-4} +37 z^4-3 a^5 z^3-a^3 z^3+12 a z^3+21 z^3 a^{-1} +8 z^3 a^{-3} -3 z^3 a^{-5} +2 a^4 z^2-11 a^2 z^2-13 z^2 a^{-2} +z^2 a^{-4} -27 z^2+2 a^5 z-7 a z-9 z a^{-1} -3 z a^{-3} +z a^{-5} +4 a^2+4 a^{-2} +9$ The A2 invariant $-q^{14}-2 q^{10}+4 q^2+1+4 q^{-2} -2 q^{-10} - q^{-14}$ The G2 invariant $q^{80}-q^{78}+3 q^{76}-4 q^{74}+3 q^{72}-q^{70}-3 q^{68}+8 q^{66}-11 q^{64}+13 q^{62}-11 q^{60}+3 q^{58}+4 q^{56}-14 q^{54}+21 q^{52}-25 q^{50}+21 q^{48}-15 q^{46}-3 q^{44}+18 q^{42}-33 q^{40}+35 q^{38}-29 q^{36}+11 q^{34}+8 q^{32}-27 q^{30}+32 q^{28}-22 q^{26}+4 q^{24}+17 q^{22}-28 q^{20}+22 q^{18}-2 q^{16}-21 q^{14}+41 q^{12}-41 q^{10}+34 q^8-4 q^6-24 q^4+51 q^2-55+51 q^{-2} -23 q^{-4} -5 q^{-6} +34 q^{-8} -41 q^{-10} +44 q^{-12} -25 q^{-14} +3 q^{-16} +19 q^{-18} -30 q^{-20} +23 q^{-22} -5 q^{-24} -17 q^{-26} +32 q^{-28} -32 q^{-30} +14 q^{-32} +7 q^{-34} -31 q^{-36} +41 q^{-38} -40 q^{-40} +21 q^{-42} - q^{-44} -20 q^{-46} +30 q^{-48} -31 q^{-50} +23 q^{-52} -10 q^{-54} -2 q^{-56} +8 q^{-58} -14 q^{-60} +12 q^{-62} -9 q^{-64} +6 q^{-66} - q^{-68} -2 q^{-70} +3 q^{-72} -3 q^{-74} +2 q^{-76} - q^{-78} + q^{-80}$