The two most famous isotomic pivotal cubics K007 = Lucas cubic and K008 = Droussent cubic generate a pencil of cubics we call the Lucas - Droussent pencil. Each member of this pencil is an isotomic pK with pivot on the line X4, X69 and isopivot on the Jerabek hyperbola. These cubics are : – the isogonal conjugates of pKs with pole X32, pivot on the Euler line. See Table 34. – the complements of pKs with pole on the Brocard axis, pivot G i.e. the cubics of the pencil generated by K002 = Thomson cubic and K043 = Droussent medial cubic. The nine base points of the pencil are A, B, C, G, H, X69, Ga, Gb, Gc (vertices of the antimedial triangle). The following table presents a selection of these cubics according to the pivot P or the isopivot P* or the third point Q on the line X2, X69. The base points are omitted.
 centers on the cubic cubic pivot P X4 X193, X487, X488, X2996 K170 X69 X7, X8, X20, X189, X253, X329, X1032, X1034 K007 X76 X6, X22, X76, X1670, X1671 K141 X264 X3, X254, X264, X1993 K045 X286 X21, X63, X72, X92, X286, X1441, X2997 K610 X311 X54, X311, X1994, X2888 X314 X1, X65, X75, X81, X314, X321, X1764, X2995 K254 X315 X66, X315, X1370 X316 X67, X316, X524, X671, X858, X2373 K008 X317 X68, X317 X340 X30, X265, X340, X1494, X2986 K611 X511 X290, X385, X401, X511, X1916, X1972 K355 X621 X616, X621, X628, X2992 K1053a X622 X617, X622, X627, X2993 K1053b X877 X877, X879 X1232 X1173, X1232, X2889 X1234 X1175, X1234 X1235 X1176, X1235 X1236 X1177, X1236, X2892 X1330 X1330, X1654 X1843 X384, X1843 X3260 X74, X94, X146, X323, X1138, X1272, X2071 K279 X5207 X147, X1031, X2896 K1000 X14615 X64, X394, X2052 K235 X18906 X194, X263, X2998, X3212 K1037 isopivot P* X3 X3, X254, X264, X1993 X6 X6, X22, X76, X1670, X1671 K141 X54 X54, X311, X1994, X2888 X64 X64, X394, X2052 K235 X65 X1, X65, X75, X81, X314, X321, X1764, X2995 K254 X66 X66, X315, X1370 X67 X67, X316, X524, X671, X858, X2373 K008 X72 X21, X63, X72, X92, X286, X1441, X2997 K610 X74 X74, X94, X146, X323, X1138, X1272, X2071 K279 X248 X248, X393, X1297, X2987 X265 X30, X265, X340, X1494, X2986 K611 X290 X290, X385, X401, X511, X1916, X1972 K355 X1173 X1173, X1232, X2889 X1177 X1177, X1236, X2892 X1439 X1439, X1817, X1895 X1903 X1446, X1903, X2184, X2287 X2574 X1113, X2574, X2592 X2575 X1114, X2575, X2593 X2992 X616, X621, X628, X2992 point Q X6 X6, X22, X76, X1670, X1671 K141 X81 X1, X65, X75, X81, X314, X321, X1764, X2995 K254 X141 X83, X141, X1369 X193 X193, X487, X488, X2996 K170 X323 X74, X94, X146, X323, X1138, X1272, X2071 K279 X385 X290, X385, X401, X511, X1916, X1972 K355 X394 X64, X394, X2052 K235 X524 X67, X316, X524, X671, X858, X2373 K008 X1993 X3, X254, X264, X1993 K045 X1994 X54, X311, X1994, X2888 X2287 X1446, X1903, X2184, X2287