These are the pivotal cubics with pivot X(1), the incenter of ABC, and isopivot P*. All these cubics contain A, B, C, X(1), the vertices of the incentral triangle. For any P* on the cubic K702 = psK+(X1125, X75, X1), the cubic pK(X1 x P*, X1) has concurring asymptotes and is therefore a pK+. This is the case when P* is X(1) giving a decomposed cubic, X(8) giving K157, X(79) giving K097, X(274), X(1125). The table gives cubics passing through at least seven centers of ETC and some special other cubics. The pole W is the barycentric product X(1) x P*.
 P* W Cubic or centers on the cubic X2 X1 K101 X6 X31 X1, X6, X55, X57, X365, X1419, X2067 X8 X9 K157 X31 X32 K175 X36 K206, the only circular cubic X42 X213 K362 X56 X604 K632 X71 X228 X1, X6, X55, X71, X72, X1214, X1751 X79 X2160 K097, the only equilateral cubic X210 X1334 X1, X8, X9, X37, X42, X210, X3158 X212 X1, X3, X6, X55, X212, X219, X3157 X255 X577 X1, X3, X255, X921, X1069, X1124, X1335, X3157 X350 X239 K770 X603 X1, X3, X56, X221, X603, X1433, X3157 X672 X2223 X1, X6, X55, X241, X292, X518, X672, X673 X851 X1, X65, X73, X243, X851, X1936, X2652, X2660 X902 X2251 X1, X6, X44, X55, X106, X678, X902, X1319, X2161, X2342 X922 X1, X31, X48, X896, X922, X923, X2157 X1042 X1, X34, X56, X64, X65, X73, X207, X221, X1042 X1096 X2207 X1, X19, X33, X34, X204, X207, X1096, X2331 X1109 X115 K672 X1407 X1106 X1, X56, X57, X221, X1407, X1419, X1422 X1418 X1, X57, X279, X354, X1418, X1419, X2293 X1427 X1042 X1, X57, X65, X73, X278, X1419, X1427 X1457 X1, X56, X102, X221, X517, X1411, X1457 X1464 X1, X36, X65, X73, X74, X1464, X1870 X1755 X237 X1, X31, X48, X240, X1755, X1821, X1959, X1967 X1914 X2210 K774 X1926 X1, X75, X336, X350, X1909, X1926, X1934, X1966, X3112 X1933 X14602 K861 X2151 X1, X31, X48, X1094, X1250, X2151, X2153, X2307 X2206 X1, X31, X48, X58, X501, X1474, X2206 X2238 X1, X37, X42, X238, X239, X2107, X2238 X2268 X1, X6, X55, X940, X958, X2268, X2339 X2276 X869 X1, X2, X6, X55, X192, X869, X984, X1002, X2276 X2293 X1, X6, X55, X354, X1212, X2191, X2293 X2308 X1, X6, X55, X58, X501, X1100, X1962, X2160, X2308 X2309 X1197 X1, X6, X55, X86, X893, X1107, X2309 X2594 X1, X35, X54, X65, X73, X2307, X2594, X2599 X3056 X1, X6, X55, X982, X2319, X3056, X3061 X3116 X3117 X1, X31, X48, X75, X1469, X2186, X2275, X2276, X3056, X3116