Cremona's table of elliptic curves

84042 = 2 · 3² · 7 · 23 · 29

Class	r	Atkin-Lehner	Eigenvalues
84042a (1 curve)	1	2+ 3+ 7+ 23+ 29+	2+ 3+ -1 7+ -5 -1 -8 -6
Curve Equation t Generators 84042a1 [1,-1,0,-17092899600,860944240063744] 1 [1786340448:472861855184:12167]
84042b (1 curve)	2	2+ 3+ 7+ 23- 29+	2+ 3+ -1 7+ -3 -5  2  0
Curve Equation t Generators 84042b1 [1,-1,0,-15,97] 1 [-4:11:1]&[6:11:1]
84042c (1 curve)	2	2+ 3+ 7+ 23- 29+	2+ 3+ -3 7+ -1 -1 -4  2
Curve Equation t Generators 84042c1 [1,-1,0,174,38996] 1 [20:-234:1]&[-29:109:1]
84042d (1 curve)	0	2+ 3+ 7- 23+ 29+	2+ 3+  1 7-  1 -1  0  2
Curve Equation t 84042d1 [1,-1,0,-25044,-1519228] 1
84042e (2 curves)	1	2+ 3+ 7- 23+ 29-	2+ 3+ -2 7- -4  2 -6  0
Curve Equation t Generators 84042e1 [1,-1,0,567,10829] 2 [-7:84:1] 84042e2 [1,-1,0,-5313,129605] 2 [7:301:1]
84042f (2 curves)	1	2+ 3+ 7- 23- 29+	2+ 3+ -3 7-  3 -1 -6  8
Curve Equation t Generators 84042f1 [1,-1,0,-26286,1696788] 3 [84:-318:1] 84042f2 [1,-1,0,125859,5707781] 1 [1162:40891:1]
84042g (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3-  0 7+ -4  0  4  0
Curve Equation t 84042g1 [1,-1,0,-579087,175957677] 2 84042g2 [1,-1,0,-9359127,11022819093] 2
84042h (1 curve)	2	2+ 3- 7+ 23+ 29+	2+ 3-  1 7+  1 -7  6 -6
Curve Equation t Generators 84042h1 [1,-1,0,261,-203] 1 [2:17:1]&[3:23:1]
84042i (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3-  2 7+  0  0  2  4
Curve Equation t 84042i1 [1,-1,0,-3141,59157] 2 84042i2 [1,-1,0,-13581,-548451] 2
84042j (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3-  2 7+ -2 -4 -2  0
Curve Equation t 84042j1 [1,-1,0,-77526,8216032] 2 84042j2 [1,-1,0,-153216,-10388570] 2
84042k (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3- -2 7+ -4  0  6  4
Curve Equation t 84042k1 [1,-1,0,-3554313,2580063245] 2 84042k2 [1,-1,0,-3596073,2516362541] 2
84042l (4 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3- -2 7+ -4  6 -6  4
Curve Equation t 84042l1 [1,-1,0,-405168,-100078336] 2 84042l2 [1,-1,0,-6499248,-6375761920] 4 84042l3 [1,-1,0,-6515808,-6341625136] 2 84042l4 [1,-1,0,-103987968,-408126777040] 2
84042m (1 curve)	0	2+ 3- 7+ 23+ 29+	2+ 3-  3 7+  5  3  4  0
Curve Equation t 84042m1 [1,-1,0,-4703304753,-125498146835043] 1
84042n (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3-  4 7+  4 -4  0  0
Curve Equation t 84042n1 [1,-1,0,-706455,-235211747] 2 84042n2 [1,-1,0,-11397015,-14806445027] 2
84042o (2 curves)	0	2+ 3- 7+ 23+ 29+	2+ 3- -4 7+  4  2 -2  6
Curve Equation t 84042o1 [1,-1,0,-511299,141738709] 2 84042o2 [1,-1,0,-8195139,9031941589] 2
84042p (2 curves)	1	2+ 3- 7+ 23+ 29-	2+ 3-  0 7+ -4 -2 -4  0
Curve Equation t Generators 84042p1 [1,-1,0,828,0] 2 [4:56:1] 84042p2 [1,-1,0,-3312,2484] 2 [-50:228:1]
84042q (1 curve)	1	2+ 3- 7+ 23+ 29-	2+ 3-  3 7+  5 -5  8  0
Curve Equation t Generators 84042q1 [1,-1,0,-32058,-4752972] 1 [241:1094:1]
84042r (4 curves)	1	2+ 3- 7+ 23- 29+	2+ 3-  2 7+  0 -2  2  0
Curve Equation t Generators 84042r1 [1,-1,0,113679,-5807075] 2 [5858:446135:1] 84042r2 [1,-1,0,-491841,-47830163] 4 [-4767:158611:27] 84042r3 [1,-1,0,-4297221,3396038737] 2 [827:19769:1] 84042r4 [1,-1,0,-6374781,-6188442935] 2 [2232660636635:155134707788657:365525875]
84042s (4 curves)	1	2+ 3- 7+ 23- 29+	2+ 3- -2 7+ -4  2 -6 -4
Curve Equation t Generators 84042s1 [1,-1,0,-155223,-26738019] 2 [583:8690:1] 84042s2 [1,-1,0,-2577303,-1591886115] 4 [-929:591:1] 84042s3 [1,-1,0,-2671263,-1469493819] 2 [-1181:6674:1] 84042s4 [1,-1,0,-41236623,-101912821515] 2 [-4934347:2466886:1331]
84042t (2 curves)	0	2+ 3- 7- 23- 29+	2+ 3-  0 7-  0 -2 -2 -6
Curve Equation t 84042t1 [1,-1,0,-7047,-334611] 2 84042t2 [1,-1,0,-127107,-17407143] 2
84042u (1 curve)	0	2+ 3- 7- 23- 29+	2+ 3-  1 7-  3  1  2  2
Curve Equation t 84042u1 [1,-1,0,-3189429,-2408918859] 1
84042v (1 curve)	0	2+ 3- 7- 23- 29+	2+ 3-  1 7-  3  1 -6 -6
Curve Equation t 84042v1 [1,-1,0,-7957629,8685346581] 1
84042w (2 curves)	0	2+ 3- 7- 23- 29+	2+ 3-  2 7-  6 -2  6 -8
Curve Equation t 84042w1 [1,-1,0,-23751,-1112643] 2 84042w2 [1,-1,0,-357831,-82294083] 2
84042x (4 curves)	0	2+ 3- 7- 23- 29+	2+ 3- -2 7-  0 -2  2 -4
Curve Equation t 84042x1 [1,-1,0,-42813,-2753595] 2 84042x2 [1,-1,0,-648333,-200758635] 4 84042x3 [1,-1,0,-611793,-224414631] 2 84042x4 [1,-1,0,-10373193,-12856691439] 2
84042y (2 curves)	0	2+ 3- 7- 23- 29+	2+ 3-  4 7-  0 -2  6  6
Curve Equation t 84042y1 [1,-1,0,-659295,2424464973] 2 84042y2 [1,-1,0,-31394655,67245339213] 2
84042z (1 curve)	1	2+ 3- 7- 23- 29-	2+ 3- -1 7- -1 -5  4  4
Curve Equation t Generators 84042z1 [1,-1,0,-9450,-501368] 1 [266:-4102:1]
84042ba (1 curve)	1	2+ 3- 7- 23- 29-	2+ 3-  3 7- -5 -5  0  0
Curve Equation t Generators 84042ba1 [1,-1,0,139482,-49436492] 1 [38380:570634:125]
84042bb (1 curve)	1	2- 3+ 7+ 23+ 29-	2- 3+  1 7+  3 -5 -2  0
Curve Equation t Generators 84042bb1 [1,-1,1,-137,-2483] 1 [158:295:8]
84042bc (1 curve)	1	2- 3+ 7+ 23+ 29-	2- 3+  3 7+  1 -1  4  2
Curve Equation t Generators 84042bc1 [1,-1,1,19,-1451] 1 [31:152:1]
84042bd (1 curve)	0	2- 3+ 7+ 23- 29-	2- 3+  1 7+  5 -1  8 -6
Curve Equation t 84042bd1 [1,-1,1,-153836096402,-23245340645624687] 1
84042be (2 curves)	0	2- 3+ 7- 23+ 29-	2- 3+  3 7- -3 -1  6  8
Curve Equation t 84042be1 [1,-1,1,13984,-216061] 3 84042be2 [1,-1,1,-236576,-45576701] 1
84042bf (2 curves)	0	2- 3+ 7- 23- 29+	2- 3+  2 7-  4  2  6  0
Curve Equation t 84042bf1 [1,-1,1,5101,-297485] 2 84042bf2 [1,-1,1,-47819,-3451517] 2
84042bg (1 curve)	1	2- 3+ 7- 23- 29-	2- 3+ -1 7- -1 -1  0  2
Curve Equation t Generators 84042bg1 [1,-1,1,-2783,57195] 1 [35:24:1]
84042bh (2 curves)	0	2- 3- 7+ 23+ 29-	2- 3-  0 7+  4 -4  4 -4
Curve Equation t 84042bh1 [1,-1,1,520,-521] 2 84042bh2 [1,-1,1,-2090,-2609] 2
84042bi (2 curves)	0	2- 3- 7+ 23+ 29-	2- 3-  2 7+ -2  2  4 -2
Curve Equation t 84042bi1 [1,-1,1,17644576,21921285251] 2 84042bi2 [1,-1,1,-90597344,197013415043] 2
84042bj (4 curves)	0	2- 3- 7+ 23+ 29-	2- 3-  2 7+  4  2 -2  4
Curve Equation t 84042bj1 [1,-1,1,-44035394,-112462679887] 2 84042bj2 [1,-1,1,-44035574,-112461714367] 4 84042bj3 [1,-1,1,-42657764,-119829139999] 2 84042bj4 [1,-1,1,-45416264,-105032497615] 2
84042bk (1 curve)	2	2- 3- 7+ 23+ 29-	2- 3- -3 7+ -1 -3 -2 -6
Curve Equation t Generators 84042bk1 [1,-1,1,-365054,84989837] 1 [697:-13341:1]&[-465:12643:1]
84042bl (4 curves)	1	2- 3- 7+ 23- 29-	2- 3- -2 7+  4  2 -6 -4
Curve Equation t Generators 84042bl1 [1,-1,1,-446,-157363] 2 [93:727:1] 84042bl2 [1,-1,1,-46526,-3806899] 4 [-129:253:1] 84042bl3 [1,-1,1,-88286,4110797] 2 [-195:3823:1] 84042bl4 [1,-1,1,-742046,-245847859] 2 [-497:253:1]
84042bm (2 curves)	1	2- 3- 7+ 23- 29-	2- 3- -4 7+  0  6 -4 -4
Curve Equation t Generators 84042bm1 [1,-1,1,-390542,-102317155] 2 [1161:-32333:1] 84042bm2 [1,-1,1,-6403982,-6236025955] 2 [-1463:915:1]
84042bn (1 curve)	1	2- 3- 7- 23+ 29-	2- 3-  1 7-  1 -1  4  4
Curve Equation t Generators 84042bn1 [1,-1,1,-3888707,111906214467] 1 [45395:9645786:1]
84042bo (1 curve)	1	2- 3- 7- 23+ 29-	2- 3- -1 7-  3 -1  0  4
Curve Equation t Generators 84042bo1 [1,-1,1,8437,279195] 1 [5:564:1]
84042bp (2 curves)	1	2- 3- 7- 23+ 29-	2- 3-  2 7-  0  2  0 -6
Curve Equation t Generators 84042bp1 [1,-1,1,346,8741] 2 [3:97:1] 84042bp2 [1,-1,1,-4874,121493] 2 [61:189:1]
84042bq (2 curves)	1	2- 3- 7- 23+ 29-	2- 3-  2 7- -2  2 -4  6
Curve Equation t Generators 84042bq1 [1,-1,1,-17834,-3006759] 2 [243:2517:1] 84042bq2 [1,-1,1,-440654,-112263447] 2 [1701:62849:1]
84042br (2 curves)	1	2- 3- 7- 23+ 29-	2- 3-  2 7- -4  4  2 -4
Curve Equation t Generators 84042br1 [1,-1,1,-14009,-629607] 2 [-69:104:1] 84042br2 [1,-1,1,-24449,443625] 2 [-135:1194:1]
84042bs (2 curves)	1	2- 3- 7- 23+ 29-	2- 3- -2 7-  2  2  0  6
Curve Equation t Generators 84042bs1 [1,-1,1,-356141,82058005] 2 [463:-4264:1] 84042bs2 [1,-1,1,-5701421,5241322261] 2 [1391:-1480:1]
84042bt (2 curves)	1	2- 3- 7- 23+ 29-	2- 3- -2 7-  4 -4 -2  4
Curve Equation t Generators 84042bt1 [1,-1,1,-78370646,-266240076699] 2 [-3768111:21576547:729] 84042bt2 [1,-1,1,-113490806,-3906529563] 2 [-811:296379:1]
84042bu (2 curves)	1	2- 3- 7- 23+ 29-	2- 3- -2 7- -4 -4  0 -6
Curve Equation t Generators 84042bu1 [1,-1,1,-464231,-121629473] 2 [1309:38234:1] 84042bu2 [1,-1,1,-7427711,-7789813649] 2 [3977:157888:1]
84042bv (4 curves)	0	2- 3- 7- 23- 29-	2- 3-  0 7-  0  2  0 -4
Curve Equation t 84042bv1 [1,-1,1,380515,-1141567] 2 84042bv2 [1,-1,1,-1522175,-7991251] 2 84042bv3 [1,-1,1,-5156240,4839839795] 6 84042bv4 [1,-1,1,-84176600,297278388083] 6
84042bw (2 curves)	0	2- 3- 7- 23- 29-	2- 3-  2 7- -4  2  0  2
Curve Equation t 84042bw1 [1,-1,1,-97230254,-370974886995] 2 84042bw2 [1,-1,1,-1558000274,-23669672397987] 2
84042bx (1 curve)	0	2- 3- 7- 23- 29-	2- 3-  3 7-  5 -5 -4  0
Curve Equation t 84042bx1 [1,-1,1,44194,-7504387] 1

Data from Elliptic Curve Data by J. E. Cremona.
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