Cremona's table of elliptic curves

86814 = 2 · 3² · 7 · 13 · 53

Class	r	Atkin-Lehner	Eigenvalues
86814a (2 curves)	1	2+ 3+ 7+ 13+ 53+	2+ 3+  2 7+  0 13+ -2  8
Curve Equation t Generators 86814a1 [1,-1,0,-336,-21248] 2 [207:2854:1] 86814a2 [1,-1,0,-13776,-615296] 2 [27795:323342:125]
86814b (2 curves)	2	2+ 3+ 7+ 13+ 53-	2+ 3+ -2 7+  2 13+ -6 -6
Curve Equation t Generators 86814b1 [1,-1,0,387,-860335] 2 [107:577:1]&[172:-2153:1] 86814b2 [1,-1,0,-133383,-18384205] 2 [-227:511:1]&[2165:98100:1]
86814c (2 curves)	0	2+ 3+ 7+ 13- 53+	2+ 3+  2 7+  0 13-  2  0
Curve Equation t 86814c1 [1,-1,0,548949,-231268303] 2 86814c2 [1,-1,0,-3988941,-2426699485] 2
86814d (1 curve)	1	2+ 3+ 7+ 13- 53-	2+ 3+  1 7+ -3 13-  1 -3
Curve Equation t Generators 86814d1 [1,-1,0,-65814,-9192844] 1 [331:2116:1]
86814e (2 curves)	0	2+ 3+ 7- 13- 53-	2+ 3+ -2 7-  0 13- -4  2
Curve Equation t 86814e1 [1,-1,0,-957003,362441285] 2 86814e2 [1,-1,0,-15333963,23115418181] 2
86814f (1 curve)	0	2+ 3- 7+ 13+ 53+	2+ 3- -1 7+  3 13+ -5  5
Curve Equation t 86814f1 [1,-1,0,141255,-63548051] 1
86814g (1 curve)	2	2+ 3- 7+ 13+ 53+	2+ 3- -3 7+ -1 13+ -7  3
Curve Equation t Generators 86814g1 [1,-1,0,-7686,261468] 1 [51:-12:1]&[-57:744:1]
86814h (1 curve)	0	2+ 3- 7+ 13+ 53+	2+ 3- -3 7+  3 13+  5  7
Curve Equation t 86814h1 [1,-1,0,-190006341651,-34004599243217739] 1
86814i (1 curve)	1	2+ 3- 7+ 13+ 53-	2+ 3-  1 7+ -2 13+  3 -4
Curve Equation t Generators 86814i1 [1,-1,0,-2816199,2162395521] 1 [-1650:48939:1]
86814j (1 curve)	1	2+ 3- 7+ 13+ 53-	2+ 3-  3 7+  1 13+  1 -3
Curve Equation t Generators 86814j1 [1,-1,0,-21708,-56302128] 1 [9513099:239873616:12167]
86814k (1 curve)	1	2+ 3- 7+ 13+ 53-	2+ 3-  3 7+  1 13+  7 -6
Curve Equation t Generators 86814k1 [1,-1,0,-243,-19467] 1 [31:30:1]
86814l (1 curve)	1	2+ 3- 7+ 13+ 53-	2+ 3-  3 7+ -3 13+ -3  1
Curve Equation t Generators 86814l1 [1,-1,0,-243,5103] 1 [81:675:1]
86814m (1 curve)	1	2+ 3- 7+ 13+ 53-	2+ 3- -3 7+  2 13+  1 -4
Curve Equation t Generators 86814m1 [1,-1,0,-126,-8424] 1 [42:-264:1]
86814n (1 curve)	1	2+ 3- 7+ 13- 53+	2+ 3-  1 7+  3 13- -3  7
Curve Equation t Generators 86814n1 [1,-1,0,-4149,137781] 1 [51:213:1]
86814o (4 curves)	1	2+ 3- 7+ 13- 53+	2+ 3-  2 7+  0 13-  2  4
Curve Equation t Generators 86814o1 [1,-1,0,-47556,3268944] 2 [44805:686676:125] 86814o2 [1,-1,0,-231876,-39972528] 4 [1371:46407:1] 86814o3 [1,-1,0,226044,-178722288] 2 [592:12444:1] 86814o4 [1,-1,0,-3638916,-2670888816] 2 [2203:-354:1]
86814p (1 curve)	0	2+ 3- 7+ 13- 53-	2+ 3-  1 7+  1 13- -1  7
Curve Equation t 86814p1 [1,-1,0,-63999,-6544139] 1
86814q (1 curve)	1	2+ 3- 7- 13+ 53+	2+ 3- -1 7-  2 13+  3 -4
Curve Equation t Generators 86814q1 [1,-1,0,-1485,22437] 1 [18:27:1]
86814r (1 curve)	1	2+ 3- 7- 13+ 53+	2+ 3- -1 7-  5 13+  3  2
Curve Equation t Generators 86814r1 [1,-1,0,88605,52838109] 1 [537:15702:1]
86814s (2 curves)	2	2+ 3- 7- 13+ 53-	2+ 3- -2 7- -4 13+  0 -6
Curve Equation t Generators 86814s1 [1,-1,0,-4338,113620] 2 [36:-74:1]&[-13:416:1] 86814s2 [1,-1,0,-69858,7124260] 2 [-205:3680:1]&[-64:3398:1]
86814t (1 curve)	1	2+ 3- 7- 13- 53-	2+ 3- -1 7- -3 13- -5  6
Curve Equation t Generators 86814t1 [1,-1,0,2340,200434] 1 [-13:416:1]
86814u (2 curves)	1	2+ 3- 7- 13- 53-	2+ 3-  3 7-  0 13-  3 -4
Curve Equation t Generators 86814u1 [1,-1,0,-33633,-3609603] 1 [1842:77703:1] 86814u2 [1,-1,0,275247,56824173] 3 [-174:1995:1]
86814v (2 curves)	1	2+ 3- 7- 13- 53-	2+ 3-  3 7-  3 13- -3 -1
Curve Equation t Generators 86814v1 [1,-1,0,12339522,4532412348] 1 [83571:24138780:1] 86814v2 [1,-1,0,-200040048,1127755758762] 3 [-195:132763269:125]
86814w (1 curve)	1	2+ 3- 7- 13- 53-	2+ 3- -3 7-  3 13-  3  1
Curve Equation t Generators 86814w1 [1,-1,0,-162261,-62691809] 1 [1139:34490:1]
86814x (2 curves)	0	2- 3+ 7+ 13+ 53+	2- 3+  2 7+ -2 13+  6 -6
Curve Equation t 86814x1 [1,-1,1,3481,23225563] 2 86814x2 [1,-1,1,-1200449,497573983] 2
86814y (2 curves)	1	2- 3+ 7+ 13+ 53-	2- 3+ -2 7+  0 13+  2  8
Curve Equation t Generators 86814y1 [1,-1,1,-3026,576721] 2 [17:-737:1] 86814y2 [1,-1,1,-123986,16736977] 2 [-167:5807:1]
86814z (1 curve)	1	2- 3+ 7+ 13- 53+	2- 3+ -1 7+  3 13- -1 -3
Curve Equation t Generators 86814z1 [1,-1,1,-7313,342913] 1 [-19:-680:1]
86814ba (2 curves)	0	2- 3+ 7+ 13- 53-	2- 3+ -2 7+  0 13- -2  0
Curve Equation t 86814ba1 [1,-1,1,60994,8545161] 2 86814ba2 [1,-1,1,-443216,90025497] 2
86814bb (2 curves)	0	2- 3+ 7- 13- 53+	2- 3+  2 7-  0 13-  4  2
Curve Equation t 86814bb1 [1,-1,1,-106334,-13388307] 2 86814bb2 [1,-1,1,-1703774,-855558675] 2
86814bc (2 curves)	1	2- 3- 7+ 13+ 53+	2- 3-  0 7+ -4 13+  2  6
Curve Equation t Generators 86814bc1 [1,-1,1,27310,-936367] 2 [681:17911:1] 86814bc2 [1,-1,1,-125330,-7896751] 2 [-207:3127:1]
86814bd (1 curve)	1	2- 3- 7+ 13+ 53+	2- 3- -3 7+  3 13+  7 -7
Curve Equation t Generators 86814bd1 [1,-1,1,5340676,-2449191873] 1 [1409:88017:1]
86814be (1 curve)	0	2- 3- 7+ 13+ 53-	2- 3-  0 7+ -5 13+  4  0
Curve Equation t 86814be1 [1,-1,1,13855,-112759] 1
86814bf (2 curves)	0	2- 3- 7+ 13+ 53-	2- 3- -2 7+  6 13+ -6 -2
Curve Equation t 86814bf1 [1,-1,1,-100571,-21787509] 2 86814bf2 [1,-1,1,-1935131,-1035198453] 2
86814bg (1 curve)	0	2- 3- 7+ 13- 53+	2- 3- -1 7+  3 13- -7 -5
Curve Equation t 86814bg1 [1,-1,1,-138592508,-627974673217] 1
86814bh (1 curve)	2	2- 3- 7- 13+ 53+	2- 3- -1 7- -3 13+ -7 -7
Curve Equation t Generators 86814bh1 [1,-1,1,-1643,721595] 1 [75:970:1]&[-65:774:1]
86814bi (4 curves)	0	2- 3- 7- 13+ 53+	2- 3-  2 7- -4 13+ -6  8
Curve Equation t 86814bi1 [1,-1,1,-824,-52549] 2 86814bi2 [1,-1,1,-26744,-1669957] 4 86814bi3 [1,-1,1,-40784,284411] 2 86814bi4 [1,-1,1,-427424,-107449477] 2
86814bj (1 curve)	1	2- 3- 7- 13- 53+	2- 3- -4 7-  3 13-  4 -4
Curve Equation t Generators 86814bj1 [1,-1,1,-977,14145] 1 [3:104:1]
86814bk (1 curve)	0	2- 3- 7- 13- 53-	2- 3- -1 7- -5 13-  3 -3
Curve Equation t 86814bk1 [1,-1,1,-4497638,-3670217355] 1
86814bl (2 curves)	0	2- 3- 7- 13- 53-	2- 3-  3 7- -6 13-  3 -4
Curve Equation t 86814bl1 [1,-1,1,-11772581,-15544380067] 1 86814bl2 [1,-1,1,-11688476,-15777486241] 3

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations