Cremona's table of elliptic curves

68800 = 2⁶ · 5² · 43

Class	r	Atkin-Lehner	Eigenvalues
68800a (1 curve)	1	2+ 5+ 43+	2+  0 5+ -1  4 -1  0 -1
Curve Equation t Generators 68800a1 [0,0,0,-32300,2238000] 1 [-10:1600:1]
68800b (1 curve)	1	2+ 5+ 43+	2+  0 5+  2  1 -1  3  2
Curve Equation t Generators 68800b1 [0,0,0,-800,-11750] 1 [9855:978325:1]
68800c (1 curve)	1	2+ 5+ 43+	2+  0 5+  2 -5 -7  6 -4
Curve Equation t Generators 68800c1 [0,0,0,32500,3350000] 1 [4520:267292:125]
68800d (1 curve)	1	2+ 5+ 43+	2+  0 5+ -2 -1  1 -2 -4
Curve Equation t Generators 68800d1 [0,0,0,-327500,72950000] 1 [904:22708:1]
68800e (1 curve)	1	2+ 5+ 43+	2+  0 5+ -2 -4  2 -1 -8
Curve Equation t Generators 68800e1 [0,0,0,-1250,18750] 1 [29:83:1]
68800f (1 curve)	1	2+ 5+ 43+	2+  1 5+  2 -1  4 -5  3
Curve Equation t Generators 68800f1 [0,1,0,-23553,1525343] 1 [3455:118336:125]
68800g (1 curve)	1	2+ 5+ 43+	2+  1 5+  2  5 -2 -5  3
Curve Equation t Generators 68800g1 [0,1,0,219167,-63569537] 1 [12211162530:777806032813:3048625]
68800h (1 curve)	1	2+ 5+ 43+	2+  1 5+ -2  1  2  3  3
Curve Equation t Generators 68800h1 [0,1,0,-120833,-16249537] 1 [910761169:71123129524:148877]
68800i (1 curve)	1	2+ 5+ 43+	2+ -1 5+ -4  3  2 -5  1
Curve Equation t Generators 68800i1 [0,-1,0,-14753,694657] 1 [93:344:1]
68800j (1 curve)	1	2+ 5+ 43+	2+  2 5+  2  3 -1 -5 -2
Curve Equation t Generators 68800j1 [0,-1,0,417,7037] 1 [-5699484:18534457:531441]
68800k (1 curve)	1	2+ 5+ 43+	2+  2 5+  2  3  5  2 -8
Curve Equation t Generators 68800k1 [0,-1,0,-115833,-15135463] 1 [884486806994212757179895973:39072720033330909112700105464:439226801236474117809111]
68800l (1 curve)	1	2+ 5+ 43+	2+  2 5+  2 -3  5 -7 -2
Curve Equation t Generators 68800l1 [0,-1,0,-16383,1279637] 1 [-1872476:4424775:12167]
68800m (1 curve)	1	2+ 5+ 43+	2+  2 5+  2 -4  2  3 -6
Curve Equation t Generators 68800m1 [0,-1,0,7,-13] 1 [994:1653:343]
68800n (1 curve)	1	2+ 5+ 43+	2+ -2 5+  0 -3 -5  3  2
Curve Equation t Generators 68800n1 [0,1,0,-33,313] 1 [8:25:1]
68800o (1 curve)	1	2+ 5+ 43+	2+ -2 5+  2  3  1  2  0
Curve Equation t Generators 68800o1 [0,1,0,7,103] 1 [-3:8:1]
68800p (1 curve)	1	2+ 5+ 43+	2+ -2 5+  2 -3  1  5  6
Curve Equation t Generators 68800p1 [0,1,0,-802383,-304014137] 1 [70233841598868883482:212917183981583354125:66942703664637319]
68800q (1 curve)	1	2+ 5+ 43+	2+ -2 5+ -2  1 -7 -3  6
Curve Equation t Generators 68800q1 [0,1,0,217,1063] 1 [-2:25:1]
68800r (1 curve)	1	2+ 5+ 43+	2+ -2 5+ -3  2 -1  6  1
Curve Equation t Generators 68800r1 [0,1,0,-33,-31937] 1 [73:600:1]
68800s (1 curve)	1	2+ 5+ 43+	2+ -2 5+  4 -3 -1 -2  0
Curve Equation t Generators 68800s1 [0,1,0,-193,-1377] 1 [77:668:1]
68800t (1 curve)	1	2+ 5+ 43+	2+ -2 5+ -4 -1 -5  7  0
Curve Equation t Generators 68800t1 [0,1,0,-13,-27] 1 [4:1:1]
68800u (1 curve)	1	2+ 5+ 43+	2+ -2 5+ -4  5  7 -2  0
Curve Equation t Generators 68800u1 [0,1,0,-2622273,1633554463] 1 [717:11068:1]
68800v (1 curve)	1	2+ 5+ 43+	2+ -2 5+  5  2 -5 -2 -3
Curve Equation t Generators 68800v1 [0,1,0,-2264033,1326280063] 1 [2473:104200:1]
68800w (1 curve)	1	2+ 5+ 43+	2+  3 5+  4 -1 -4 -1  1
Curve Equation t Generators 68800w1 [0,0,0,-3340,-74320] 1 [17922:459928:27]
68800x (1 curve)	1	2+ 5+ 43+	2+  3 5+ -4 -5  2  3  5
Curve Equation t Generators 68800x1 [0,0,0,-940,-18640] 1 [4818:63296:27]
68800y (1 curve)	1	2+ 5+ 43+	2+ -3 5+  2  1  2  3 -1
Curve Equation t Generators 68800y1 [0,0,0,-778060,264162160] 1 [509:43:1]
68800z (1 curve)	0	2+ 5+ 43-	2+  0 5+  0  3  3 -2  4
Curve Equation t 68800z1 [0,0,0,-80,-280] 1
68800ba (1 curve)	0	2+ 5+ 43-	2+  0 5+  2 -1 -1  7  6
Curve Equation t 68800ba1 [0,0,0,400,4000] 1
68800bb (1 curve)	0	2+ 5+ 43-	2+  0 5+  2  4  2 -1  8
Curve Equation t 68800bb1 [0,0,0,-1250,-18750] 1
68800bc (1 curve)	0	2+ 5+ 43-	2+  0 5+  3  0 -3  4  1
Curve Equation t 68800bc1 [0,0,0,25300,-386000] 1
68800bd (1 curve)	0	2+ 5+ 43-	2+  1 5+  4 -3  2 -5 -1
Curve Equation t 68800bd1 [0,1,0,-14753,-694657] 1
68800be (1 curve)	0	2+ 5+ 43-	2+ -1 5+  2 -1  2  3 -3
Curve Equation t 68800be1 [0,-1,0,-120833,16249537] 1
68800bf (1 curve)	0	2+ 5+ 43-	2+  2 5+  2 -1 -7 -3 -6
Curve Equation t 68800bf1 [0,-1,0,217,-1063] 1
68800bg (1 curve)	0	2+ 5+ 43-	2+  2 5+ -2  3  1  5 -6
Curve Equation t 68800bg1 [0,-1,0,-802383,304014137] 1
68800bh (1 curve)	0	2+ 5+ 43-	2+  2 5+ -2 -3  1  2  0
Curve Equation t 68800bh1 [0,-1,0,7,-103] 1
68800bi (1 curve)	0	2+ 5+ 43-	2+  2 5+ -2  4 -6 -5 -6
Curve Equation t 68800bi1 [0,-1,0,-19813,-1129923] 1
68800bj (1 curve)	0	2+ 5+ 43-	2+  2 5+  4 -5  3 -2  0
Curve Equation t 68800bj1 [0,-1,0,1667,17037] 1
68800bk (3 curves)	0	2+ 5+ 43-	2+ -2 5+  1  6  5  6  7
Curve Equation t 68800bk1 [0,1,0,6367,1004863] 1 68800bk2 [0,1,0,-57633,-27987137] 1 68800bk3 [0,1,0,-9001633,-10398211137] 1
68800bl (1 curve)	0	2+ 5+ 43-	2+ -2 5+ -2  3  5 -7  2
Curve Equation t 68800bl1 [0,1,0,-16383,-1279637] 1
68800bm (1 curve)	0	2+ 5+ 43-	2+ -2 5+ -2 -3 -1 -5  2
Curve Equation t 68800bm1 [0,1,0,417,-7037] 1
68800bn (1 curve)	0	2+ 5+ 43-	2+ -2 5+ -2 -3  5  2  8
Curve Equation t 68800bn1 [0,1,0,-115833,15135463] 1
68800bo (2 curves)	0	2+ 5+ 43-	2+ -2 5+  4  3 -1  3 -2
Curve Equation t 68800bo1 [0,1,0,-1333,18963] 1 68800bo2 [0,1,0,6667,58963] 1
68800bp (1 curve)	0	2+ 5+ 43-	2+ -3 5+  0 -3  0  7  7
Curve Equation t 68800bp1 [0,0,0,132500,-2450000] 1
68800bq (1 curve)	2	2+ 5+ 43-	2+ -3 5+ -4  1 -4 -1 -1
Curve Equation t Generators 68800bq1 [0,0,0,-3340,74320] 1 [-14:344:1]&[34:8:1]
68800br (1 curve)	0	2+ 5- 43+	2+  0 5-  0  3 -3  2  4
Curve Equation t 68800br1 [0,0,0,-2000,-35000] 1
68800bs (1 curve)	0	2+ 5- 43+	2+  0 5- -2  4 -2  1  8
Curve Equation t 68800bs1 [0,0,0,-50,-150] 1
68800bt (1 curve)	2	2+ 5- 43+	2+  1 5- -2 -1 -2 -3 -3
Curve Equation t Generators 68800bt1 [0,1,0,-4833,128063] 1 [921:1720:27]&[-53:488:1]
68800bu (1 curve)	0	2+ 5- 43+	2+ -1 5- -4 -3 -2  5 -1
Curve Equation t 68800bu1 [0,-1,0,-368833,-86094463] 1
68800bv (1 curve)	0	2+ 5- 43+	2+  2 5-  2 -3  1  5  2
Curve Equation t 68800bv1 [0,-1,0,17,-63] 1
68800bw (1 curve)	0	2+ 5- 43+	2+  2 5-  2 -3 -5 -2  8
Curve Equation t 68800bw1 [0,-1,0,-4633,122937] 1
68800bx (1 curve)	0	2+ 5- 43+	2+ -2 5-  2 -3 -1 -2  0
Curve Equation t 68800bx1 [0,1,0,167,-12537] 1
68800by (1 curve)	0	2+ 5- 43+	2+ -2 5-  2  4  6  5 -6
Curve Equation t 68800by1 [0,1,0,-495333,-142231037] 1
68800bz (1 curve)	2	2+ 5- 43+	2+ -2 5- -4 -5 -3  2  0
Curve Equation t Generators 68800bz1 [0,1,0,67,163] 1 [-2:5:1]&[3:20:1]
68800ca (1 curve)	0	2+ 5- 43+	2+  3 5-  0 -3  0 -7  7
Curve Equation t 68800ca1 [0,0,0,5300,-19600] 1
68800cb (1 curve)	0	2+ 5- 43+	2+  3 5-  4  1  4  1 -1
Curve Equation t 68800cb1 [0,0,0,-83500,9290000] 1
68800cc (1 curve)	1	2+ 5- 43-	2+  0 5-  2 -1 -1  2 -4
Curve Equation t Generators 68800cc1 [0,0,0,-13100,583600] 1 [120:860:1]
68800cd (1 curve)	1	2+ 5- 43-	2+  0 5-  2 -4 -2  1 -8
Curve Equation t Generators 68800cd1 [0,0,0,-50,150] 1 [5:5:1]
68800ce (1 curve)	1	2+ 5- 43-	2+  0 5- -2 -5  7 -6 -4
Curve Equation t Generators 68800ce1 [0,0,0,1300,26800] 1 [24:268:1]
68800cf (1 curve)	1	2+ 5- 43-	2+  1 5-  4  3 -2  5  1
Curve Equation t Generators 68800cf1 [0,1,0,-368833,86094463] 1 [33:8600:1]
68800cg (1 curve)	1	2+ 5- 43-	2+ -1 5-  2  1 -2 -3  3
Curve Equation t Generators 68800cg1 [0,-1,0,-4833,-128063] 1 [157:-1720:1]
68800ch (1 curve)	1	2+ 5- 43-	2+ -1 5- -2 -1 -4  5  3
Curve Equation t Generators 68800ch1 [0,-1,0,-588833,191845537] 1 [467:4300:1]
68800ci (1 curve)	1	2+ 5- 43-	2+ -1 5- -2  5  2  5  3
Curve Equation t Generators 68800ci1 [0,-1,0,8767,-512063] 1 [177:2560:1]
68800cj (1 curve)	1	2+ 5- 43-	2+  2 5- -2  3 -1 -2  0
Curve Equation t Generators 68800cj1 [0,-1,0,167,12537] 1 [-159:2872:27]
68800ck (1 curve)	1	2+ 5- 43-	2+  2 5-  4 -1  5 -7  0
Curve Equation t Generators 68800ck1 [0,-1,0,-333,-2713] 1 [61218:542825:729]
68800cl (1 curve)	1	2+ 5- 43-	2+  2 5-  4  5 -7  2  0
Curve Equation t Generators 68800cl1 [0,-1,0,-65556833,204325421537] 1 [483479741:233565300:103823]
68800cm (1 curve)	1	2+ 5- 43-	2+  2 5- -4 -3  1  2  0
Curve Equation t Generators 68800cm1 [0,-1,0,-4833,-162463] 1 [83:36:1]
68800cn (1 curve)	1	2+ 5- 43-	2+ -2 5- -2  3  1  5 -2
Curve Equation t Generators 68800cn1 [0,1,0,17,63] 1 [-2:5:1]
68800co (1 curve)	1	2+ 5- 43-	2+ -2 5- -2  3 -5 -2 -8
Curve Equation t Generators 68800co1 [0,1,0,-4633,-122937] 1 [109:824:1]
68800cp (1 curve)	1	2+ 5- 43-	2+ -2 5- -2 -4 -2 -3 -6
Curve Equation t Generators 68800cp1 [0,1,0,167,-1287] 1 [8:25:1]
68800cq (1 curve)	1	2+ 5- 43-	2+  3 5- -2  1 -2 -3 -1
Curve Equation t Generators 68800cq1 [0,0,0,-19451500,33020270000] 1 [8589210:1626112:3375]
68800cr (1 curve)	1	2+ 5- 43-	2+ -3 5-  4 -5 -2 -3  5
Curve Equation t Generators 68800cr1 [0,0,0,-23500,-2330000] 1 [5772:41968:27]
68800cs (1 curve)	1	2+ 5- 43-	2+ -3 5- -4 -1  4  1  1
Curve Equation t Generators 68800cs1 [0,0,0,-83500,-9290000] 1 [500:8600:1]
68800ct (1 curve)	2	2- 5+ 43+	2-  0 5+  0 -3  3 -2 -4
Curve Equation t Generators 68800ct1 [0,0,0,-80,280] 1 [6:4:1]&[9:17:1]
68800cu (1 curve)	0	2- 5+ 43+	2-  0 5+ -2  1 -1  7 -6
Curve Equation t 68800cu1 [0,0,0,400,-4000] 1
68800cv (1 curve)	2	2- 5+ 43+	2-  0 5+ -3  0 -3  4 -1
Curve Equation t Generators 68800cv1 [0,0,0,25300,386000] 1 [10:800:1]&[74:1632:1]
68800cw (3 curves)	0	2- 5+ 43+	2-  2 5+ -1 -6  5  6 -7
Curve Equation t 68800cw1 [0,-1,0,6367,-1004863] 1 68800cw2 [0,-1,0,-57633,27987137] 1 68800cw3 [0,-1,0,-9001633,10398211137] 1
68800cx (1 curve)	0	2- 5+ 43+	2-  2 5+  2  3 -5  3  6
Curve Equation t 68800cx1 [0,-1,0,-603,-5503] 1
68800cy (1 curve)	0	2- 5+ 43+	2-  2 5+  2  5  1  1 -2
Curve Equation t 68800cy1 [0,-1,0,-3883,-91863] 1
68800cz (1 curve)	0	2- 5+ 43+	2-  2 5+  3  2  7  2 -1
Curve Equation t 68800cz1 [0,-1,0,-5633,183137] 1
68800da (2 curves)	0	2- 5+ 43+	2-  2 5+ -4 -3 -1  3  2
Curve Equation t 68800da1 [0,-1,0,-1333,-18963] 1 68800da2 [0,-1,0,6667,-58963] 1
68800db (1 curve)	0	2- 5+ 43+	2- -2 5+  2 -4 -6 -5  6
Curve Equation t 68800db1 [0,1,0,-19813,1129923] 1
68800dc (1 curve)	0	2- 5+ 43+	2- -2 5+ -4  5  3 -2  0
Curve Equation t 68800dc1 [0,1,0,1667,-17037] 1
68800dd (1 curve)	0	2- 5+ 43+	2-  3 5+  0  3  0  7 -7
Curve Equation t 68800dd1 [0,0,0,132500,2450000] 1
68800de (1 curve)	1	2- 5+ 43-	2-  0 5+  1 -4 -1  0  1
Curve Equation t Generators 68800de1 [0,0,0,-32300,-2238000] 1 [330:4800:1]
68800df (1 curve)	1	2- 5+ 43-	2-  0 5+  2  1  1 -2  4
Curve Equation t Generators 68800df1 [0,0,0,-327500,-72950000] 1 [35271900:1615594624:15625]
68800dg (1 curve)	1	2- 5+ 43-	2-  0 5+ -2 -1 -1  3 -2
Curve Equation t Generators 68800dg1 [0,0,0,-800,11750] 1 [-5:125:1]
68800dh (1 curve)	1	2- 5+ 43-	2-  0 5+ -2  5 -7  6  4
Curve Equation t Generators 68800dh1 [0,0,0,32500,-3350000] 1 [1053564:1081412512:1]
68800di (1 curve)	1	2- 5+ 43-	2- -1 5+ -2  1  4 -5 -3
Curve Equation t Generators 68800di1 [0,-1,0,-23553,-1525343] 1 [208:1591:1]
68800dj (1 curve)	1	2- 5+ 43-	2- -1 5+ -2 -5 -2 -5 -3
Curve Equation t Generators 68800dj1 [0,-1,0,219167,63569537] 1 [653:22016:1]
68800dk (1 curve)	1	2- 5+ 43-	2-  2 5+  0  3 -5  3 -2
Curve Equation t Generators 68800dk1 [0,-1,0,-33,-313] 1 [7218:11125:729]
68800dl (1 curve)	1	2- 5+ 43-	2-  2 5+  3 -2 -1  6 -1
Curve Equation t Generators 68800dl1 [0,-1,0,-33,31937] 1 [152:1875:1]
68800dm (1 curve)	1	2- 5+ 43-	2-  2 5+  4  1 -5  7  0
Curve Equation t Generators 68800dm1 [0,-1,0,-13,27] 1 [66:53:27]
68800dn (1 curve)	1	2- 5+ 43-	2-  2 5+  4 -5  7 -2  0
Curve Equation t Generators 68800dn1 [0,-1,0,-2622273,-1633554463] 1 [17267601949644026246935222483609677113668053444584566681:320709979804431717962100730739218413129226339792029598462848:50057728243108449099057239594040257939134764911]
68800do (1 curve)	1	2- 5+ 43-	2-  2 5+ -4  3 -1 -2  0
Curve Equation t Generators 68800do1 [0,-1,0,-193,1377] 1 [-9:48:1]
68800dp (1 curve)	1	2- 5+ 43-	2-  2 5+ -5 -2 -5 -2  3
Curve Equation t Generators 68800dp1 [0,-1,0,-2264033,-1326280063] 1 [294129532688648:24301567860712125:41027927849]
68800dq (1 curve)	1	2- 5+ 43-	2- -2 5+ -2 -3 -5  3 -6
Curve Equation t Generators 68800dq1 [0,1,0,-603,5503] 1 [14:1:1]
68800dr (1 curve)	1	2- 5+ 43-	2- -2 5+ -2  4  2  3  6
Curve Equation t Generators 68800dr1 [0,1,0,7,13] 1 [4:11:1]
68800ds (1 curve)	1	2- 5+ 43-	2- -2 5+ -2 -5  1  1  2
Curve Equation t Generators 68800ds1 [0,1,0,-3883,91863] 1 [38:25:1]
68800dt (1 curve)	1	2- 5+ 43-	2- -2 5+ -3 -2  7  2  1
Curve Equation t Generators 68800dt1 [0,1,0,-5633,-183137] 1 [123:1000:1]
68800du (1 curve)	1	2- 5+ 43-	2-  3 5+ -2 -1  2  3  1
Curve Equation t Generators 68800du1 [0,0,0,-778060,-264162160] 1 [152332958193942:6956622105325568:62240377347]
68800dv (1 curve)	1	2- 5+ 43-	2- -3 5+  4  5  2  3 -5
Curve Equation t Generators 68800dv1 [0,0,0,-940,18640] 1 [-16:172:1]
68800dw (1 curve)	1	2- 5- 43+	2-  0 5-  2  5  7 -6  4
Curve Equation t Generators 68800dw1 [0,0,0,1300,-26800] 1 [29420:456152:125]
68800dx (1 curve)	1	2- 5- 43+	2-  0 5- -2  1 -1  2  4
Curve Equation t Generators 68800dx1 [0,0,0,-13100,-583600] 1 [220:2680:1]
68800dy (1 curve)	1	2- 5- 43+	2-  1 5-  2  1 -4  5 -3
Curve Equation t Generators 68800dy1 [0,1,0,-588833,-191845537] 1 [4583:305600:1]
68800dz (1 curve)	1	2- 5- 43+	2-  1 5-  2 -5  2  5 -3
Curve Equation t Generators 68800dz1 [0,1,0,8767,512063] 1 [113:1720:1]
68800ea (1 curve)	1	2- 5- 43+	2-  2 5-  2 -3  5 -3 -6
Curve Equation t Generators 68800ea1 [0,-1,0,-15083,718037] 1 [1884:575:27]
68800eb (1 curve)	1	2- 5- 43+	2-  2 5-  2  4 -2 -3  6
Curve Equation t Generators 68800eb1 [0,-1,0,167,1287] 1 [18:99:1]
68800ec (1 curve)	1	2- 5- 43+	2- -2 5-  4  3  1  2  0
Curve Equation t Generators 68800ec1 [0,1,0,-4833,162463] 1 [33:200:1]
68800ed (1 curve)	1	2- 5- 43+	2- -2 5- -4  1  5 -7  0
Curve Equation t Generators 68800ed1 [0,1,0,-333,2713] 1 [8:25:1]
68800ee (1 curve)	1	2- 5- 43+	2- -2 5- -4 -5 -7  2  0
Curve Equation t Generators 68800ee1 [0,1,0,-65556833,-204325421537] 1 [30433:5097800:1]
68800ef (1 curve)	1	2- 5- 43+	2-  3 5- -4  5 -2 -3 -5
Curve Equation t Generators 68800ef1 [0,0,0,-23500,2330000] 1 [678:35776:27]
68800eg (1 curve)	1	2- 5- 43+	2- -3 5-  2 -1 -2 -3  1
Curve Equation t Generators 68800eg1 [0,0,0,-19451500,-33020270000] 1 [510929202070676:76831990312878016:21740999671]
68800eh (1 curve)	2	2- 5- 43-	2-  0 5-  0 -3 -3  2 -4
Curve Equation t Generators 68800eh1 [0,0,0,-2000,35000] 1 [-50:100:1]&[25:25:1]
68800ei (1 curve)	0	2- 5- 43-	2-  2 5- -2 -4  6  5  6
Curve Equation t 68800ei1 [0,-1,0,-495333,142231037] 1
68800ej (1 curve)	0	2- 5- 43-	2-  2 5-  4  5 -3  2  0
Curve Equation t 68800ej1 [0,-1,0,67,-163] 1
68800ek (1 curve)	0	2- 5- 43-	2- -2 5- -2  3  5 -3  6
Curve Equation t 68800ek1 [0,1,0,-15083,-718037] 1
68800el (1 curve)	2	2- 5- 43-	2- -3 5-  0  3  0 -7 -7
Curve Equation t Generators 68800el1 [0,0,0,5300,19600] 1 [50:-640:1]&[5:215:1]

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

Part of Computational Number Theory
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