(* Here are the equations of some elliptic curves with small conductor. The names are those used in the Swinnerton-Dyer tables, from the Antwerp proceedings of the conference on modular forms, volume 4, Lecture Notes in Mathematics 476. They are useful for experiments in number theory. Copyright 1990, Wolfram Research, Inc. *) Curve11A = { y^2 + y == x^3 - x^2, 11, { 1/5 , 0 } } Curve11B = { y^2 + y == x^3 - x^2 - 10x - 20 , 11, { 1/5 , 0 } } Curve14A = { y^2 + x y + y == x^3 - x, 14, { 1/6 , 0 } } Curve14B = { y^2 + x y + y == x^3 - 11x + 12 , 14, { 1/3 , 0 } } Curve14C = { y^2 + x y + y == x^3 + 4x - 6 , 14, { 1/6 , 0 } } Curve14D = { y^2 + x y + y == x^3 - 36x - 70 , 14, { 1/3 , 0 } } Curve15A = { y^2 + x y + y == x^3 + x^2, 15, { 1/4 , 0 } } Curve15B = { y^2 + x y + y == x^3 + x^2 - 5x + 2 , 15, { 1/4 , 0 } } Curve15C = { y^2 + x y + y == x^3 + x^2 - 10x - 10 , 15, { 1/4 , 0 } } Curve15D = { y^2 + x y + y == x^3 + x^2 - 80x + 242 , 15, { 1/4 , 0 } } Curve15E = { y^2 + x y + y == x^3 + x^2 - 135x - 660 , 15, { 1/2 , 0 } } Curve15F = { y^2 + x y + y == x^3 + x^2 + 35x - 28 , 15, { 1/4 , 0 } } Curve17A = { y^2 + x y + y == x^3 - x^2 - x, 17, { 1/2 , 0 } } Curve17B = { y^2 + x y + y == x^3 - x^2 - 6x - 4 , 17, { 1/2 , 0 } } Curve17C = { y^2 + x y + y == x^3 - x^2 - x - 14 , 17, { 1/4 , 0 } } Curve19A = { y^2 + y == x^3 + x^2 + x, 19, { 1/3 , 0 } } Curve19B = { y^2 + y == x^3 + x^2 - 9x - 15 , 19, { 1/3 , 0 } } Curve20A = { y^2 == x^3 + x^2 - x, 20, { 1/3 , 0 } } Curve20B = { y^2 == x^3 + x^2 + 4x + 4 , 20, { 1/6 , 0 } } Curve21A = { y^2 + x y == x^3 + x, 21, { 1/4 , 0 } } Curve21B = { y^2 + x y == x^3 - 4x - 1 , 21, { 1/4 , 0 } } Curve21C = { y^2 + x y == x^3 - 39x + 90 , 21, { 1/4 , 0 } } Curve21D = { y^2 + x y == x^3 - 49x - 136 , 21, { 1/2 , 0 } } Curve24A = { y^2 == x^3 - x^2 + x, 24, { 1/4 , 0 } } Curve24B = { y^2 == x^3 - x^2 - 4x + 4 , 24, { 1/4 , 0 } } Curve24C = { y^2 == x^3 - x^2 - 24x - 36 , 24, { 1/2 , 0 } } Curve24D = { y^2 == x^3 - x^2 - 64x + 220 , 24, { 1/2 , 0 } } Curve26A = { y^2 + x y + y == x^3, 26, { 1/3 , 0 } } Curve26B = { y^2 + x y + y == x^3 - 5x - 8 , 26, { 1/3 , 0 } } Curve26D = { y^2 + x y + y == x^3 - x^2 - 3x + 3 , 26, { 1/7 , 0 } } Curve30A = { y^2 + x y + y == x^3 + x + 2 , 30, { 1/6 , 0 } } Curve30B = { y^2 + x y + y == x^3 - 19x + 26 , 30, { 1/6 , 0 } } Curve30D = { y^2 + x y + y == x^3 - 69x - 194 , 30, { 1/3 , 1/2 } } Curve30E = { y^2 + x y + y == x^3 - 289x + 1862 , 30, { 1/6 , 0 } } Curve30F = { y^2 + x y + y == x^3 - 334x - 2368 , 30, { 1/2 , 0 } } Curve32A = { y^2 == x^3 - x, 32, { 1/2 , 0 } } Curve32B = { y^2 == x^3 + 4x, 32, { 1/4 , 0 } } Curve32D = { y^2 == x^3 - 11x + 14 , 32, { 1/4 , 1/2 } } Curve36A = { y^2 == x^3 + 1 , 36, { 1/6 , 0 } } Curve38A = { y^2 + x y + y == x^3 + x^2 + 1 , 38, { 1/5 , 0 } } Curve42A = { y^2 + x y + y == x^3 + x^2 - 4x + 5 , 42, { 1/8 , 0 } } Curve48E = { y^2 == x^3 + x^2 + 16x + 180 , 48, { 1/8 , 0 } } Curve50A = { y^2 + x y + y == x^3 + x^2 - 3x + 1 , 50, { 1/5 , 0 } } Curve50B = { y^2 + x y + y == x^3 + x^2 + 22x - 9 , 50, { 1/5 , 0 } } Curve54B = { y^2 + x y + y == x^3 - x^2 - 14x + 29 , 54, { 1/9 , 0 } } Curve57F = { y^2 + y == x^3 + x^2 + 20x - 32 , 57, { 1/5 , 0 } } Curve58B = { y^2 + x y + y == x^3 + x^2 + 5x + 9 , 58, { 1/5 , 0 } } Curve66B = { y^2 + x y + y == x^3 + 4x + 20 , 66, { 1/6 , 0 } } Curve66J = { y^2 + x y == x^3 + 115x + 561 , 66, { 1/10 , 0 } } Curve84C = { y^2 == x^3 + x^2 + 7x, 84, { 1/6 , 0 } } Curve90A = { y^2 + x y + y == x^3 - x^2 - 8x + 11 , 90, { 1/6 , 0 } } Curve90G = { y^2 + x y + y == x^3 - x^2 - 122x + 1721 , 90, { 1/12 , 0 } } Curve90M = { y^2 + x y == x^3 - x^2 + 6x, 90, { 1/6 , 0 } } Curve102B = { y^2 + x y + y == x^3 - 216x + 2062 , 102, { 1/6 , 0 } } Curve106E = { y^2 + x y == x^3 - 283x - 2351 , 106, { 1/3 , 0 } } Curve110C = { y^2 + x y + y == x^3 + x^2 + 10x - 45 , 110, { 1/5 , 0 } } Curve114B = { y^2 + x y == x^3 + 32x + 8 , 114, { 1/6 , 0 } } Curve117A = { y^2 + x y + y == x^3 - x^2 + 4x + 6 , 117, { 1/4 , 0 } } Curve118B = { y^2 + x y + y == x^3 + x^2 - 25x + 39 , 118, { 1/5 , 0 } } Curve123A = { y^2 + y == x^3 + x^2 - 10x + 10 , 123, { 1/5 , 0 } } Curve124B = { y^2 == x^3 + x^2 - 2x + 1 , 124, { 1/3 , 0 } } Curve126C = { y^2 + x y + y == x^3 - x^2 + 40x + 155 , 126, { 1/6 , 0 } } Curve126E = { y^2 + x y + y == x^3 - x^2 - 1535x + 23591 , 126, { 1/6 , 0 } } Curve130F = { y^2 + x y + y == x^3 - 13x + 156 , 130, { 1/6 , 0 } } Curve138G = { y^2 + x y + y == x^3 - 36x + 82 , 138, { 1/6 , 0 } } Curve150C = { y^2 + x y == x^3 - 28x + 272 , 150, { 1/10 , 0 } } Curve155D = { y^2 + y == x^3 - x^2 + 10x + 6 , 155, { 1/5 , 0 } } Curve162K = { y^2 + x y == x^3 - x^2 - 6x + 8 , 162, { 1/3 , 0 } } Curve170I = { y^2 + x y + y == x^3 - 2474x + 52716 , 170, { 1/6 , 0 } } Curve171B = { y^2 + y == x^3 - 84x + 315 , 171, { 1/3 , 0 } } Curve172A = { y^2 == x^3 + x^2 - 13x + 15 , 172, { 1/3 , 0 } } Curve174B = { y^2 + x y + y == x^3 - 20x - 34 , 174, { 1/2 , 0 } } Curve174G = { y^2 + x y == x^3 - x + 137 , 174, { 1/7 , 0 } } Curve175A = { y^2 + y == x^3 - x^2 - 148x + 748 , 175, { 1/5 , 0 } } Curve178A = { y^2 + x y == x^3 + 6x - 28 , 178, { 1/3 , 0 } } Curve180C = { y^2 == x^3 - 372x + 2761 , 180, { 1/6 , 1/2 } } Curve180D = { y^2 == x^3 - 327x + 3454 , 180, { 1/6 , 0 } } Curve182A = { y^2 + x y == x^3 + 7x - 7 , 182, { 1/3 , 0 } } Curve182B = { y^2 + x y == x^3 - 193x - 1055 , 182, { 1/3 , 0 } } Curve182E = { y^2 + x y + y == x^3 - x^2 + 866x + 6445 , 182, { 1/4 , 0 } } Curve182F = { y^2 + x y + y == x^3 - x^2 - 4254x + 59693 , 182, { 1/2 , 0 } } Curve186B = { y^2 + x y == x^3 + 15x + 9 , 186, { 1/5 , 0 } } Curve189C = { y^2 + y == x^3 - 24x + 45 , 189, { 1/3 , 0 } } Curve189D = { y^2 + y == x^3 - 54x - 88 , 189, { 1/3 , 0 } } Curve192R = { y^2 == x^3 - x^2 - 9x + 9 , 192, { 1/2 , 0 } } Curve192T = { y^2 == x^3 - x^2 - 129x + 609 , 192, { 1/4 , 1/2 } } Curve198J = { y^2 + x y == x^3 - x^2 - 198x + 1120 , 198, { 1/2 , 0 } } Curves = Hold[{ Curve11A, Curve11B, Curve14A, Curve14B, Curve14C, Curve14D, Curve15A, Curve15B, Curve15C, Curve15D, Curve15E, Curve15F, Curve17A, Curve17B, Curve17C, Curve19A, Curve19B, Curve20A, Curve20B, Curve21A, Curve21B, Curve21C, Curve21D, Curve24A, Curve24B, Curve24C, Curve24D, Curve26A, Curve26B, Curve26D, Curve30A, Curve30B, Curve30D, Curve30E, Curve30F, Curve32A, Curve32B, Curve32D, Curve36A, Curve38A, Curve42A, Curve48E, Curve50A, Curve50B, Curve54B, Curve57F, Curve58B, Curve66B, Curve66J, Curve84C, Curve90A, Curve90G, Curve90M, Curve102B, Curve106E, Curve110C, Curve114B, Curve117A, Curve118B, Curve123A, Curve124B, Curve126C, Curve126E, Curve130F, Curve138G, Curve150C, Curve155D, Curve162K, Curve170I, Curve171B, Curve172A, Curve174B, Curve174G, Curve175A, Curve178A, Curve180C, Curve180D, Curve182A, Curve182B, Curve182E, Curve182F, Curve186B, Curve189C, Curve189D, Curve192R, Curve192T, Curve198J }]