Cremona's table of elliptic curves

86490 = 2 · 3² · 5 · 31²

Class	r	Atkin-Lehner	Eigenvalues
86490a (2 curves)	0	2+ 3+ 5+ 31-	2+ 3+ 5+  0 -2  6 -2 -4
Curve Equation t 86490a1 [1,-1,0,-135587670,633370195700] 2 86490a2 [1,-1,0,-2194741590,39575677299956] 2
86490b (1 curve)	0	2+ 3+ 5+ 31-	2+ 3+ 5+ -3 -5  0 -2 -1
Curve Equation t 86490b1 [1,-1,0,-14595,7117181] 1
86490c (1 curve)	0	2+ 3+ 5- 31+	2+ 3+ 5-  1 -1 -4  0 -6
Curve Equation t 86490c1 [1,-1,0,-7591119,8059820525] 1
86490d (1 curve)	0	2+ 3+ 5- 31+	2+ 3+ 5-  1  5  2  6  0
Curve Equation t 86490d1 [1,-1,0,-97749031974,-11763023329856332] 1
86490e (1 curve)	0	2+ 3+ 5- 31+	2+ 3+ 5- -3  1 -6 -2  8
Curve Equation t 86490e1 [1,-1,0,5586,-3262580] 1
86490f (2 curves)	1	2+ 3+ 5- 31-	2+ 3+ 5-  0 -4 -6 -4  8
Curve Equation t Generators 86490f1 [1,-1,0,-113973819,274056740325] 2 [13741:1134317:1] 86490f2 [1,-1,0,358376901,1960065400293] 2 [36867:8061174:1]
86490g (1 curve)	1	2+ 3+ 5- 31-	2+ 3+ 5-  1  1  4  0 -6
Curve Equation t Generators 86490g1 [1,-1,0,-7899,-268507] 1 [4057:256294:1]
86490h (1 curve)	1	2+ 3+ 5- 31-	2+ 3+ 5-  1 -5 -2 -6  0
Curve Equation t Generators 86490h1 [1,-1,0,-101715954,394877826260] 1 [5821:-4598:1]
86490i (2 curves)	1	2+ 3+ 5- 31-	2+ 3+ 5- -1  3  4 -6 -1
Curve Equation t Generators 86490i1 [1,-1,0,538941,-57131435] 1 [3635:221615:1] 86490i2 [1,-1,0,-6164034,6918282260] 1 [251860:13236775:64]
86490j (4 curves)	1	2+ 3+ 5- 31-	2+ 3+ 5-  2 -6  4  6 -4
Curve Equation t Generators 86490j1 [1,-1,0,5586,-45152] 2 [39:-500:1] 86490j2 [1,-1,0,-23244,-350750] 2 [-109:992:1] 86490j3 [1,-1,0,-66489,7532333] 2 [622:13143:8] 86490j4 [1,-1,0,-1104369,446970725] 2 [12244:990853:64]
86490k (1 curve)	1	2+ 3+ 5- 31-	2+ 3+ 5- -3 -1  6  2  8
Curve Equation t Generators 86490k1 [1,-1,0,6,108] 1 [-3:9:1]
86490l (2 curves)	1	2+ 3+ 5- 31-	2+ 3+ 5-  4  4 -2  0  0
Curve Equation t Generators 86490l1 [1,-1,0,-66489,4314905] 2 [27505:54959:125] 86490l2 [1,-1,0,192981,29587283] 2 [-20934595:312741679:166375]
86490m (1 curve)	1	2+ 3+ 5- 31-	2+ 3+ 5- -5  1  4  6  3
Curve Equation t Generators 86490m1 [1,-1,0,-165089409,-918972519715] 1 [732489130142977440390940202107869562277:163851707897077290856553457468618195888287:13650945399755932758165560353845293]
86490n (1 curve)	0	2+ 3- 5+ 31+	2+ 3- 5+  0  1 -6  1  4
Curve Equation t 86490n1 [1,-1,0,-1513755,19174723461] 1
86490o (1 curve)	0	2+ 3- 5+ 31+	2+ 3- 5+ -1 -5  4  2 -2
Curve Equation t 86490o1 [1,-1,0,-5535540,-5054922450] 1
86490p (1 curve)	0	2+ 3- 5+ 31+	2+ 3- 5+  5  1  4 -4  4
Curve Equation t 86490p1 [1,-1,0,-129915,19610181] 1
86490q (1 curve)	1	2+ 3- 5+ 31-	2+ 3- 5+  0 -1  6 -1  4
Curve Equation t Generators 86490q1 [1,-1,0,-1575,-643235] 1 [110990:679337:1000]
86490r (6 curves)	1	2+ 3- 5+ 31-	2+ 3- 5+  0 -4 -6  2  4
Curve Equation t Generators 86490r1 [1,-1,0,518760,-814942400] 2 [7566:178807:8] 86490r2 [1,-1,0,-10551960,-12463553984] 4 [-662032:-8807224:343] 86490r3 [1,-1,0,-32001480,54334541200] 2 [1472:101324:1] 86490r4 [1,-1,0,-166233960,-824905639184] 4 [-1119189494332:449585735801:150568768] 86490r5 [1,-1,0,-163639260,-851904530564] 2 [2315167809588917057852:-1593951982133987108773561:4887727059742912] 86490r6 [1,-1,0,-2659740660,-52796068384604] 2 [-433227562484361456243589948:216623826222780691950712889:14549922438042274115392]
86490s (1 curve)	1	2+ 3- 5+ 31-	2+ 3- 5+ -1  5 -4 -2 -2
Curve Equation t Generators 86490s1 [1,-1,0,-5760,171166] 1 [53:86:1]
86490t (2 curves)	1	2+ 3- 5+ 31-	2+ 3- 5+  2  4 -2  4  0
Curve Equation t Generators 86490t1 [1,-1,0,-22963275,-41827711419] 2 [64303189322255887786720434:6344193801944987221081979943:5344705860267527178859] 86490t2 [1,-1,0,-366155595,-2696694860475] 2 [5695974883410:1126983485598495:118370771]
86490u (2 curves)	1	2+ 3- 5+ 31-	2+ 3- 5+  2 -4  2 -4  0
Curve Equation t Generators 86490u1 [1,-1,0,-23895,1410205] 2 [78:89:1] 86490u2 [1,-1,0,-381015,90618781] 2 [318:1081:1]
86490v (1 curve)	1	2+ 3- 5+ 31-	2+ 3- 5+  5 -1 -4  4  4
Curve Equation t Generators 86490v1 [1,-1,0,-124848495,-583208114675] 1 [703006728645425295478783360210705902655:490003444970190338344542025165603157762110:1444194114881242275670495038122699]
86490w (1 curve)	1	2+ 3- 5+ 31-	2+ 3- 5+ -5  3  2 -4  7
Curve Equation t Generators 86490w1 [1,-1,0,-1476168255,-32445397598675] 1 [146323752727965004747182333508:49259287346128536387563761897315:1149712110072358609848128]
86490x (1 curve)	1	2+ 3- 5+ 31-	2+ 3- 5+ -5 -3 -2  4  7
Curve Equation t Generators 86490x1 [1,-1,0,-1536075,1089497061] 1 [225:27369:1]
86490y (2 curves)	1	2+ 3- 5- 31+	2+ 3- 5- -3  3 -2  4  0
Curve Equation t Generators 86490y1 [1,-1,0,-484524,-130633520] 1 [2519:119687:1] 86490y2 [1,-1,0,-2214324,12963191368] 1 [4007:-263566:1]
86490z (1 curve)	1	2+ 3- 5- 31+	2+ 3- 5- -3 -5  6 -8 -4
Curve Equation t Generators 86490z1 [1,-1,0,-35296749,82938903205] 1 [6689:378872:1]
86490ba (2 curves)	1	2+ 3- 5- 31+	2+ 3- 5-  4  3 -2 -3  0
Curve Equation t Generators 86490ba1 [1,-1,0,-441279,-124362995] 1 [3256457185:2649582282325:4913] 86490ba2 [1,-1,0,-13847229,29755354603] 1 [1667:105479:1]
86490bb (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  0  2  0  2 -4
Curve Equation t 86490bb1 [1,-1,0,-571014,-171437580] 2 86490bb2 [1,-1,0,-9220014,-10773381780] 2
86490bc (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  0  4  4  0  4
Curve Equation t 86490bc1 [1,-1,0,-3681864,2815539520] 2 86490bc2 [1,-1,0,-59481864,176587899520] 2
86490bd (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  0 -4 -4  0  4
Curve Equation t 86490bd1 [1,-1,0,-3538271484,-83849431668912] 2 86490bd2 [1,-1,0,-57162071484,-5260272818028912] 2
86490be (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  0 -6  2 -4  0
Curve Equation t 86490be1 [1,-1,0,337131,18364725] 2 86490be2 [1,-1,0,-1392669,150175485] 2
86490bf (4 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  2  0  4  6  8
Curve Equation t 86490bf1 [1,-1,0,12013281,-17984202035] 2 86490bf2 [1,-1,0,-73784799,-175286401907] 2 86490bf3 [1,-1,0,-342941679,-2458987043747] 2 86490bf4 [1,-1,0,-5496188859,-156832751516135] 2
86490bg (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5- -2  0 -4  6  0
Curve Equation t 86490bg1 [1,-1,0,-354789,-83347515] 2 86490bg2 [1,-1,0,-5717169,-5260189167] 2
86490bh (1 curve)	0	2+ 3- 5- 31-	2+ 3- 5-  3  5  6 -4  5
Curve Equation t 86490bh1 [1,-1,0,-199368279,1089192470085] 1
86490bi (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5- -3 -3  2 -4  0
Curve Equation t 86490bi1 [1,-1,0,-465627744,3895428215808] 1 86490bi2 [1,-1,0,-2127965544,-386169410320200] 1
86490bj (1 curve)	0	2+ 3- 5- 31-	2+ 3- 5- -3  5 -6  8 -4
Curve Equation t 86490bj1 [1,-1,0,-36729,-2774547] 1
86490bk (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5-  4 -3  2  3  0
Curve Equation t 86490bk1 [1,-1,0,-459,4293] 1 86490bk2 [1,-1,0,-14409,-995085] 1
86490bl (4 curves)	0	2+ 3- 5- 31-	2+ 3- 5- -4  0  4  0 -4
Curve Equation t 86490bl1 [1,-1,0,-916974,345165268] 2 86490bl2 [1,-1,0,-14755374,21819594388] 2 86490bl3 [1,-1,0,3926466,1477561540] 2 86490bl4 [1,-1,0,-17696034,12509361040] 2
86490bm (2 curves)	0	2+ 3- 5- 31-	2+ 3- 5- -4  4  0  0 -4
Curve Equation t 86490bm1 [1,-1,0,899316,229703040] 2 86490bm2 [1,-1,0,-4463064,2034680148] 2
86490bn (2 curves)	2	2+ 3- 5- 31-	2+ 3- 5- -4 -4  0  0 -4
Curve Equation t Generators 86490bn1 [1,-1,0,936,-7952] 2 [12:64:1]&[17:104:1] 86490bn2 [1,-1,0,-4644,-67100] 2 [-54:182:1]&[-49:227:1]
86490bo (1 curve)	0	2+ 3- 5- 31-	2+ 3- 5-  5  1  6  0 -1
Curve Equation t 86490bo1 [1,-1,0,-28359,1845693] 1
86490bp (1 curve)	0	2+ 3- 5- 31-	2+ 3- 5-  5 -1 -6  0 -1
Curve Equation t 86490bp1 [1,-1,0,-27253179,-54767015195] 1
86490bq (1 curve)	0	2- 3+ 5+ 31+	2- 3+ 5+  1  1 -4  0 -6
Curve Equation t 86490bq1 [1,-1,1,-843458,-298230719] 1
86490br (1 curve)	0	2- 3+ 5+ 31+	2- 3+ 5+  1 -5  2 -6  0
Curve Equation t 86490br1 [1,-1,1,-10861003553,435671151069937] 1
86490bs (1 curve)	0	2- 3+ 5+ 31+	2- 3+ 5+ -3 -1 -6  2  8
Curve Equation t 86490bs1 [1,-1,1,50272,88039387] 1
86490bt (2 curves)	1	2- 3+ 5+ 31-	2- 3+ 5+  0  4 -6  4  8
Curve Equation t Generators 86490bt1 [1,-1,1,-1025764373,-7398506224403] 2 [6673989:3286019920:27] 86490bt2 [1,-1,1,3225392107,-52924991200019] 2 [32346729141:16356020203472:132651]
86490bu (1 curve)	1	2- 3+ 5+ 31-	2- 3+ 5+  1 -1  4  0 -6
Curve Equation t Generators 86490bu1 [1,-1,1,-878,10237] 1 [13:23:1]
86490bv (1 curve)	1	2- 3+ 5+ 31-	2- 3+ 5+  1  5 -2  6  0
Curve Equation t Generators 86490bv1 [1,-1,1,-11301773,-14621337419] 1 [7767485:453615592:1331]
86490bw (2 curves)	1	2- 3+ 5+ 31-	2- 3+ 5+ -1 -3  4  6 -1
Curve Equation t Generators 86490bw1 [1,-1,1,-684893,-256004379] 1 [1031:11016:1] 86490bw2 [1,-1,1,4850467,1537698277] 1 [-22405:3228568:125]
86490bx (4 curves)	1	2- 3+ 5+ 31-	2- 3+ 5+  2  6  4 -6 -4
Curve Equation t Generators 86490bx1 [1,-1,1,-7388,-276513] 2 [2358:37257:8] 86490bx2 [1,-1,1,-122708,-16513569] 2 [413790:1645413:1000] 86490bx3 [1,-1,1,50272,1168831] 2 [139902086:2960421313:551368] 86490bx4 [1,-1,1,-209198,9679447] 2 [3577932883392910:12575258429364077:8108486729000]
86490by (1 curve)	1	2- 3+ 5+ 31-	2- 3+ 5+ -3  1  6 -2  8
Curve Equation t Generators 86490by1 [1,-1,1,52,-2969] 1 [55:377:1]
86490bz (2 curves)	1	2- 3+ 5+ 31-	2- 3+ 5+  4 -4 -2  0  0
Curve Equation t Generators 86490bz1 [1,-1,1,-7388,-157349] 2 [22198:1157473:8] 86490bz2 [1,-1,1,21442,-1102973] 2 [152142994:7945068235:54872]
86490ca (1 curve)	1	2- 3+ 5+ 31-	2- 3+ 5+ -5 -1  4 -6  3
Curve Equation t Generators 86490ca1 [1,-1,1,-18343268,34042133671] 1 [2953:73481:1]
86490cb (2 curves)	0	2- 3+ 5- 31-	2- 3+ 5-  0  2  6  2 -4
Curve Equation t 86490cb1 [1,-1,1,-15065297,-23453133631] 2 86490cb2 [1,-1,1,-243860177,-1465684539199] 2
86490cc (1 curve)	0	2- 3+ 5- 31-	2- 3+ 5- -3  5  0  2 -1
Curve Equation t 86490cc1 [1,-1,1,-1622,-263059] 1
86490cd (2 curves)	0	2- 3- 5+ 31-	2- 3- 5+ -1 -3 -2  0  5
Curve Equation t 86490cd1 [1,-1,1,21442,-17666769] 1 86490cd2 [1,-1,1,-4519283,-3697470309] 1
86490ce (2 curves)	0	2- 3- 5+ 31-	2- 3- 5+  2 -4  4 -6  0
Curve Equation t 86490ce1 [1,-1,1,19351957,145023660731] 2 86490ce2 [1,-1,1,-323840363,2092571438267] 2
86490cf (2 curves)	0	2- 3- 5+ 31-	2- 3- 5+ -2 -4  4  2 -8
Curve Equation t 86490cf1 [1,-1,1,4043227,-1183984419] 2 86490cf2 [1,-1,1,-17406293,-9789531843] 2
86490cg (1 curve)	0	2- 3- 5+ 31-	2- 3- 5+  3  3  2  8 -7
Curve Equation t 86490cg1 [1,-1,1,843097,163324127] 1
86490ch (2 curves)	0	2- 3- 5+ 31-	2- 3- 5+  4  2 -2  0  0
Curve Equation t 86490ch1 [1,-1,1,-118037408,494341909827] 2 86490ch2 [1,-1,1,-1889352608,31609973239107] 2
86490ci (2 curves)	0	2- 3- 5+ 31-	2- 3- 5+ -4  2 -2  0  0
Curve Equation t 86490ci1 [1,-1,1,21442,6344777] 2 86490ci2 [1,-1,1,-411008,95602457] 2
86490cj (2 curves)	0	2- 3- 5- 31+	2- 3- 5- -1  3  2 -6  2
Curve Equation t 86490cj1 [1,-1,1,229018,12727739] 1 86490cj2 [1,-1,1,-3792767,2937369791] 3
86490ck (1 curve)	0	2- 3- 5- 31+	2- 3- 5-  3  1  0 -2  2
Curve Equation t 86490ck1 [1,-1,1,36425083,24733954941] 1
86490cl (1 curve)	0	2- 3- 5- 31+	2- 3- 5- -3  3  4  4  0
Curve Equation t 86490cl1 [1,-1,1,-1111577,-1396922799] 1
86490cm (4 curves)	1	2- 3- 5- 31-	2- 3- 5-  0 -4 -6  2 -4
Curve Equation t Generators 86490cm1 [1,-1,1,-938597,-310935139] 2 [2395:104512:1] 86490cm2 [1,-1,1,-3706277,2422425629] 4 [57:46996:1] 86490cm3 [1,-1,1,5634643,12656337581] 2 [12501:1420834:1] 86490cm4 [1,-1,1,-57330077,167090390669] 2 [48284148297:-1015847595298:9129329]
86490cn (1 curve)	1	2- 3- 5- 31-	2- 3- 5-  1  5 -2 -4  1
Curve Equation t Generators 86490cn1 [1,-1,1,-89956073957,10761360678257181] 1 [800831:672145824:1]
86490co (2 curves)	1	2- 3- 5- 31-	2- 3- 5- -1 -3 -2  6  2
Curve Equation t Generators 86490co1 [1,-1,1,238,-489] 1 [22:93:8] 86490co2 [1,-1,1,-3947,-97581] 1 [77:186:1]
86490cp (2 curves)	1	2- 3- 5- 31-	2- 3- 5- -2  4  2  0  0
Curve Equation t Generators 86490cp1 [1,-1,1,-63932,-6205201] 2 [-9407640:4831993:64000] 86490cp2 [1,-1,1,-69512,-5053489] 2 [-642:767:8]
86490cq (2 curves)	1	2- 3- 5- 31-	2- 3- 5- -2 -4 -2  0  0
Curve Equation t Generators 86490cq1 [1,-1,1,-61438352,185350641891] 2 [5664109:-43856709:1331] 86490cq2 [1,-1,1,-66800732,151082888739] 2 [518436095617:206013198890187:656234909]
86490cr (1 curve)	1	2- 3- 5- 31-	2- 3- 5-  3  1 -2  0 -5
Curve Equation t Generators 86490cr1 [1,-1,1,7213,194811] 1 [101:1344:1]
86490cs (1 curve)	1	2- 3- 5- 31-	2- 3- 5-  3 -1  0  2  2
Curve Equation t Generators 86490cs1 [1,-1,1,37903,-840031] 1 [177:-3464:1]
86490ct (1 curve)	1	2- 3- 5- 31-	2- 3- 5-  3 -1  2  0 -5
Curve Equation t Generators 86490ct1 [1,-1,1,6931993,-5859078361] 1 [8409:800152:1]
86490cu (1 curve)	1	2- 3- 5- 31-	2- 3- 5- -3  3  2 -4 -3
Curve Equation t Generators 86490cu1 [1,-1,1,-1760252,-1014877249] 1 [5061:343429:1]
86490cv (1 curve)	1	2- 3- 5- 31-	2- 3- 5- -3 -3 -4 -4  0
Curve Equation t Generators 86490cv1 [1,-1,1,-1157,47189] 1 [57:-434:1]
86490cw (4 curves)	1	2- 3- 5- 31-	2- 3- 5-  4 -4 -2  2  4
Curve Equation t Generators 86490cw1 [1,-1,1,-2106212,1176933111] 4 [551:13269:1] 86490cw2 [1,-1,1,-2279192,972401559] 4 [148631:2711913:343] 86490cw3 [1,-1,1,5764378,6294027471] 2 [-242226355408:13125255274443:325660672] 86490cw4 [1,-1,1,-13090442,-17441319441] 2 [-3267573904:30402681903:1404928]
86490cx (8 curves)	1	2- 3- 5- 31-	2- 3- 5- -4  0 -2  6 -4
Curve Equation t Generators 86490cx1 [1,-1,1,12793,1706991] 2 [4342:101613:8] 86490cx2 [1,-1,1,-160187,22395399] 4 [129138:2491583:216] 86490cx3 [1,-1,1,-116942,-50342691] 2 [597:9311:1] 86490cx4 [1,-1,1,-592637,-151103541] 2 [-6615311080:-1819699797:21952000] 86490cx5 [1,-1,1,-2495417,1517876691] 2 [7198:1527:8] 86490cx6 [1,-1,1,-2884622,-1881439779] 4 [-979:2379:1] 86490cx7 [1,-1,1,-46129622,-120580315779] 2 [7851:29709:1] 86490cx8 [1,-1,1,-3922502,-405989571] 2 [-1573:44031:1]

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

Part of Computational Number Theory
Back to Tables and computations