Cremona's table of elliptic curves

88110 = 2 · 3² · 5 · 11 · 89

Class	r	Atkin-Lehner	Eigenvalues
88110a (2 curves)	1	2+ 3+ 5+ 11- 89-	2+ 3+ 5+ -1 11- -1 -6 -4
Curve Equation t Generators 88110a1 [1,-1,0,2145,-115425] 3 [633:15639:1] 88110a2 [1,-1,0,-130020,-18032104] 1 [95914468:1991286211:140608]
88110b (2 curves)	1	2+ 3+ 5+ 11- 89-	2+ 3+ 5+ -1 11-  2 -6 -7
Curve Equation t Generators 88110b1 [1,-1,0,-359025,82894365] 3 [-3226:103429:8] 88110b2 [1,-1,0,-50640,218905856] 1 [-68574:3111127:216]
88110c (1 curve)	0	2+ 3+ 5- 11+ 89+	2+ 3+ 5-  3 11+ -1 -2  5
Curve Equation t 88110c1 [1,-1,0,-84,-382] 1
88110d (1 curve)	1	2+ 3+ 5- 11+ 89-	2+ 3+ 5-  0 11+  5  0  1
Curve Equation t Generators 88110d1 [1,-1,0,-1334409,593681165] 1 [661:-668:1]
88110e (1 curve)	1	2+ 3+ 5- 11+ 89-	2+ 3+ 5-  3 11+  2 -6 -5
Curve Equation t Generators 88110e1 [1,-1,0,75396,-3959272] 1 [107:2254:1]
88110f (1 curve)	1	2+ 3+ 5- 11- 89+	2+ 3+ 5-  3 11- -1  6 -5
Curve Equation t Generators 88110f1 [1,-1,0,111,-1955] 1 [11:17:1]
88110g (1 curve)	1	2+ 3+ 5- 11- 89+	2+ 3+ 5- -3 11-  5 -2 -4
Curve Equation t Generators 88110g1 [1,-1,0,-939,11525] 1 [19:7:1]
88110h (1 curve)	2	2+ 3+ 5- 11- 89-	2+ 3+ 5- -5 11- -6 -2  1
Curve Equation t Generators 88110h1 [1,-1,0,-744,-9280] 1 [262:77:8]&[55:310:1]
88110i (1 curve)	0	2+ 3- 5+ 11+ 89+	2+ 3- 5+ -1 11+  2  6  5
Curve Equation t 88110i1 [1,-1,0,-92565,-10816619] 1
88110j (1 curve)	2	2+ 3- 5+ 11+ 89+	2+ 3- 5+ -2 11+ -1  3  0
Curve Equation t Generators 88110j1 [1,-1,0,0,-11264] 1 [23:11:1]&[32:128:1]
88110k (4 curves)	0	2+ 3- 5+ 11+ 89+	2+ 3- 5+  4 11+  2  6  0
Curve Equation t 88110k1 [1,-1,0,-380666880,2857920102400] 2 88110k2 [1,-1,0,-6090163200,182934292135936] 4 88110k3 [1,-1,0,-6089656320,182966265011200] 2 88110k4 [1,-1,0,-97442611200,11707721615451136] 2
88110l (2 curves)	1	2+ 3- 5+ 11+ 89-	2+ 3- 5+  2 11+ -2  2 -8
Curve Equation t Generators 88110l1 [1,-1,0,-2790,-45900] 2 [-39:69:1] 88110l2 [1,-1,0,-42390,-3348540] 2 [-119:69:1]
88110m (4 curves)	1	2+ 3- 5+ 11+ 89-	2+ 3- 5+ -2 11+ -6  2  0
Curve Equation t Generators 88110m1 [1,-1,0,-106585380,-410336506800] 2 [-14886233967320:-206714003016340:2305199161] 88110m2 [1,-1,0,-1690585380,-26754474106800] 2 [-54710637753514949900:14955381422381202929:2305199161000000] 88110m3 [1,-1,0,-9432763380,352620771984000] 2 [48160:-3192480:1] 88110m4 [1,-1,0,-9577709280,341224632509940] 2 [356290820:-14044180671:8000]
88110n (2 curves)	1	2+ 3- 5+ 11+ 89-	2+ 3- 5+  4 11+  6  2 -6
Curve Equation t Generators 88110n1 [1,-1,0,180,-37760] 2 [6420:37292:125] 88110n2 [1,-1,0,-15840,-745844] 2 [218:2366:1]
88110o (1 curve)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+  1 11-  2  4 -5
Curve Equation t Generators 88110o1 [1,-1,0,2790,105300] 1 [103:1164:1]
88110p (1 curve)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+ -2 11-  1 -1 -2
Curve Equation t Generators 88110p1 [1,-1,0,3150,67500] 1 [33:438:1]
88110q (1 curve)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+ -2 11- -1  7  4
Curve Equation t Generators 88110q1 [1,-1,0,-426150,-106969464] 1 [6538:522606:1]
88110r (2 curves)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+ -2 11-  4  2  4
Curve Equation t Generators 88110r1 [1,-1,0,-75169395,247407756021] 2 [-8957:-445009:1] 88110r2 [1,-1,0,-5473395,688207077621] 2 [-2717435:-164651143:343]
88110s (1 curve)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+ -3 11-  5 -6  4
Curve Equation t Generators 88110s1 [1,-1,0,-70744293135,8553851867922925] 1 [-304485961:275403878183:2197]
88110t (2 curves)	1	2+ 3- 5+ 11- 89+	2+ 3- 5+ -4 11- -6  2 -6
Curve Equation t Generators 88110t1 [1,-1,0,-26550,-1626764] 2 [-100:194:1] 88110t2 [1,-1,0,-422550,-105616364] 2 [-375:194:1]
88110u (2 curves)	0	2+ 3- 5+ 11- 89-	2+ 3- 5+  2 11-  2  2 -8
Curve Equation t 88110u1 [1,-1,0,-12825,-551075] 2 88110u2 [1,-1,0,-22725,425065] 2
88110v (1 curve)	2	2+ 3- 5+ 11- 89-	2+ 3- 5+ -2 11- -3 -1  0
Curve Equation t Generators 88110v1 [1,-1,0,-4635,124825] 1 [8:-301:1]&[-530:3235:8]
88110w (1 curve)	0	2+ 3- 5+ 11- 89-	2+ 3- 5+  3 11-  3  6 -4
Curve Equation t 88110w1 [1,-1,0,90,-324] 1
88110x (2 curves)	0	2+ 3- 5+ 11- 89-	2+ 3- 5+ -4 11- -1  6 -7
Curve Equation t 88110x1 [1,-1,0,-1087515,-436245075] 1 88110x2 [1,-1,0,-1021365,-491680665] 3
88110y (2 curves)	1	2+ 3- 5- 11+ 89+	2+ 3- 5-  2 11+  0  2  0
Curve Equation t Generators 88110y1 [1,-1,0,-153954,-22885740] 2 [-1722:4821:8] 88110y2 [1,-1,0,-9954,-64098540] 2 [18758:895701:8]
88110z (1 curve)	1	2+ 3- 5- 11+ 89+	2+ 3- 5-  2 11+ -1 -3  8
Curve Equation t Generators 88110z1 [1,-1,0,-17244,876208] 1 [77:-16:1]
88110ba (2 curves)	1	2+ 3- 5- 11+ 89+	2+ 3- 5-  2 11+ -4  2  2
Curve Equation t Generators 88110ba1 [1,-1,0,-162963339,-800683517755] 2 [48326:10182837:1] 88110ba2 [1,-1,0,-162955419,-800765241067] 2 [190522:82873489:1]
88110bb (2 curves)	1	2+ 3- 5- 11+ 89+	2+ 3- 5-  2 11+ -4  2 -4
Curve Equation t Generators 88110bb1 [1,-1,0,-1869,30833] 2 [-23:259:1] 88110bb2 [1,-1,0,381,98783] 2 [-13:309:1]
88110bc (1 curve)	1	2+ 3- 5- 11+ 89+	2+ 3- 5-  2 11+  5 -7  8
Curve Equation t Generators 88110bc1 [1,-1,0,-274908039,1754471498813] 1 [4902262341751:4385998052178799:3716672149]
88110bd (1 curve)	1	2+ 3- 5- 11+ 89+	2+ 3- 5- -2 11+  1  7  6
Curve Equation t Generators 88110bd1 [1,-1,0,-549,-34155] 1 [1959:85704:1]
88110be (2 curves)	1	2+ 3- 5- 11+ 89+	2+ 3- 5- -2 11+ -4  2 -2
Curve Equation t Generators 88110be1 [1,-1,0,-25344,0] 2 [-99:1287:1] 88110be2 [1,-1,0,101376,-76032] 2 [112:3504:1]
88110bf (2 curves)	1	2+ 3- 5- 11+ 89+	2+ 3- 5- -2 11+ -4  2  6
Curve Equation t Generators 88110bf1 [1,-1,0,-1710728964,27234960279120] 2 [23896:-7668:1] 88110bf2 [1,-1,0,-1710721044,27235225055808] 2 [26052:577464:1]
88110bg (1 curve)	1	2+ 3- 5- 11+ 89+	2+ 3- 5- -4 11+  5 -6  5
Curve Equation t Generators 88110bg1 [1,-1,0,302997861,3813517291045] 1 [178601:75772262:1]
88110bh (2 curves)	0	2+ 3- 5- 11+ 89-	2+ 3- 5- -1 11+ -1  0  5
Curve Equation t 88110bh1 [1,-1,0,29781,139725] 1 88110bh2 [1,-1,0,-424629,112902903] 3
88110bi (4 curves)	0	2+ 3- 5- 11+ 89-	2+ 3- 5-  2 11+ -4 -6 -4
Curve Equation t 88110bi1 [1,-1,0,-29586924,-61936265520] 2 88110bi2 [1,-1,0,-29946924,-60351473520] 2 88110bi3 [1,-1,0,-39431484,-17228598912] 6 88110bi4 [1,-1,0,-390993984,2959732338588] 6
88110bj (2 curves)	2	2+ 3- 5- 11- 89+	2+ 3- 5-  0 11- -4 -6 -8
Curve Equation t Generators 88110bj1 [1,-1,0,-31182534,-65127396812] 2 [-3373:42524:1]&[-2823:21349:1] 88110bj2 [1,-1,0,-495009414,-4238919959180] 2 [-12844:8402:1]&[-822636:479293:64]
88110bk (1 curve)	0	2+ 3- 5- 11- 89+	2+ 3- 5- -1 11-  2  3  4
Curve Equation t 88110bk1 [1,-1,0,-4954239,4237601805] 1
88110bl (1 curve)	0	2+ 3- 5- 11- 89+	2+ 3- 5-  3 11-  2 -5 -4
Curve Equation t 88110bl1 [1,-1,0,-50379,-3911905] 1
88110bm (1 curve)	2	2+ 3- 5- 11- 89+	2+ 3- 5- -3 11-  2  0 -5
Curve Equation t Generators 88110bm1 [1,-1,0,-49014,4271548] 1 [137:269:1]&[-133:2969:1]
88110bn (1 curve)	0	2+ 3- 5- 11- 89+	2+ 3- 5-  4 11-  5 -2 -5
Curve Equation t 88110bn1 [1,-1,0,-64899,6775893] 1
88110bo (2 curves)	2	2+ 3- 5- 11- 89+	2+ 3- 5- -4 11- -4 -6  4
Curve Equation t Generators 88110bo1 [1,-1,0,-549,4293] 2 [-26:35:1]&[-18:99:1] 88110bo2 [1,-1,0,-2529,-44415] 2 [76:407:1]&[-29:77:1]
88110bp (2 curves)	1	2+ 3- 5- 11- 89-	2+ 3- 5- -4 11- -2  2 -8
Curve Equation t Generators 88110bp1 [1,-1,0,-1539,9045] 2 [-26:189:1] 88110bp2 [1,-1,0,5661,65205] 2 [19:414:1]
88110bq (1 curve)	2	2- 3+ 5+ 11+ 89+	2- 3+ 5+ -5 11+ -6  2  1
Curve Equation t Generators 88110bq1 [1,-1,1,-83,371] 1 [-9:22:1]&[3:-14:1]
88110br (1 curve)	1	2- 3+ 5+ 11+ 89-	2- 3+ 5+  3 11+ -1 -6 -5
Curve Equation t Generators 88110br1 [1,-1,1,997,51787] 1 [-5:218:1]
88110bs (1 curve)	1	2- 3+ 5+ 11+ 89-	2- 3+ 5+ -3 11+  5  2 -4
Curve Equation t Generators 88110bs1 [1,-1,1,-8453,-302723] 1 [115:428:1]
88110bt (1 curve)	1	2- 3+ 5+ 11- 89+	2- 3+ 5+  0 11-  5  0  1
Curve Equation t Generators 88110bt1 [1,-1,1,-148268,-21938769] 1 [1061:31317:1]
88110bu (1 curve)	1	2- 3+ 5+ 11- 89+	2- 3+ 5+  3 11-  2  6 -5
Curve Equation t Generators 88110bu1 [1,-1,1,8377,143847] 1 [-15:128:1]
88110bv (1 curve)	0	2- 3+ 5+ 11- 89-	2- 3+ 5+  3 11- -1  2  5
Curve Equation t 88110bv1 [1,-1,1,-758,11071] 1
88110bw (2 curves)	1	2- 3+ 5- 11+ 89+	2- 3+ 5- -1 11+ -1  6 -4
Curve Equation t Generators 88110bw1 [1,-1,1,-14447,672671] 3 [21:604:1] 88110bw2 [1,-1,1,19303,3097171] 1 [14644:274931:64]
88110bx (2 curves)	1	2- 3+ 5- 11+ 89+	2- 3+ 5- -1 11+  2  6 -7
Curve Equation t Generators 88110bx1 [1,-1,1,-5627,-8105749] 3 [211:154:1] 88110bx2 [1,-1,1,-3231227,-2234916629] 1 [57153:515902:27]
88110by (1 curve)	1	2- 3- 5+ 11+ 89+	2- 3- 5+ -1 11+ -1  2  4
Curve Equation t Generators 88110by1 [1,-1,1,-7358,272877] 1 [5:483:1]
88110bz (1 curve)	1	2- 3- 5+ 11+ 89+	2- 3- 5+ -2 11+ -3 -7 -2
Curve Equation t Generators 88110bz1 [1,-1,1,247,-3193] 1 [1140:4609:64]
88110ca (2 curves)	1	2- 3- 5+ 11+ 89+	2- 3- 5+ -2 11+ -6  2 -2
Curve Equation t Generators 88110ca1 [1,-1,1,-8978,-289663] 2 [123:613:1] 88110ca2 [1,-1,1,12802,-1491919] 2 [1881:80761:1]
88110cb (2 curves)	0	2- 3- 5+ 11+ 89-	2- 3- 5+ -1 11+  2  3 -4
Curve Equation t 88110cb1 [1,-1,1,-2138,-34783] 1 88110cb2 [1,-1,1,-34313,2448137] 3
88110cc (4 curves)	0	2- 3- 5+ 11- 89+	2- 3- 5+  0 11-  2 -6 -8
Curve Equation t 88110cc1 [1,-1,1,-97145303,370968888687] 2 88110cc2 [1,-1,1,-1557144023,23650940478831] 4 88110cc3 [1,-1,1,-1559963543,23560994407407] 2 88110cc4 [1,-1,1,-24914304023,1513641548334831] 2
88110cd (2 curves)	0	2- 3- 5+ 11- 89+	2- 3- 5+  2 11-  5 -3  8
Curve Equation t 88110cd1 [1,-1,1,30037,-300750469] 1 88110cd2 [1,-1,1,-270338,8120442881] 3
88110ce (4 curves)	0	2- 3- 5+ 11- 89+	2- 3- 5+  4 11- -2  2  4
Curve Equation t 88110ce1 [1,-1,1,-4028,-1120129] 2 88110ce2 [1,-1,1,-188348,-31201153] 4 88110ce3 [1,-1,1,-317948,17321087] 2 88110ce4 [1,-1,1,-3007868,-2007120769] 2
88110cf (1 curve)	1	2- 3- 5+ 11- 89-	2- 3- 5+  1 11-  5  0 -1
Curve Equation t Generators 88110cf1 [1,-1,1,-2138,-38343] 1 [71:369:1]
88110cg (1 curve)	1	2- 3- 5+ 11- 89-	2- 3- 5+  3 11- -6  6  5
Curve Equation t Generators 88110cg1 [1,-1,1,-149063,-23784793] 1 [1098627343:13982261842:2048383]
88110ch (2 curves)	0	2- 3- 5- 11+ 89+	2- 3- 5- -2 11+  0 -2  6
Curve Equation t 88110ch1 [1,-1,1,-240242,-28450191] 2 88110ch2 [1,-1,1,718078,-199414479] 2
88110ci (4 curves)	0	2- 3- 5- 11+ 89+	2- 3- 5- -4 11+ -4  6  8
Curve Equation t 88110ci1 [1,-1,1,-531482,34283081] 2 88110ci2 [1,-1,1,-6520982,6402319481] 2 88110ci3 [1,-1,1,-33000017,72973926209] 6 88110ci4 [1,-1,1,-528000017,4669939926209] 6
88110cj (2 curves)	1	2- 3- 5- 11+ 89-	2- 3- 5- -1 11+  2 -6 -1
Curve Equation t Generators 88110cj1 [1,-1,1,148,-7351] 1 [134478:449351:5832] 88110cj2 [1,-1,1,-1337,199361] 3 [-59:294:1]
88110ck (2 curves)	1	2- 3- 5- 11+ 89-	2- 3- 5-  2 11+ -2 -2  6
Curve Equation t Generators 88110ck1 [1,-1,1,-8872052,10173693651] 2 [2074971:-595734619:6859] 88110ck2 [1,-1,1,-8926502,10042534491] 2 [196843852326:-57670571731729:667627624]
88110cl (2 curves)	1	2- 3- 5- 11+ 89-	2- 3- 5-  2 11+  4 -2  0
Curve Equation t Generators 88110cl1 [1,-1,1,-259682,-50300319] 2 [-309:759:1] 88110cl2 [1,-1,1,-490082,52734561] 2 [839:14799:1]
88110cm (4 curves)	1	2- 3- 5- 11+ 89-	2- 3- 5-  2 11+ -4 -6  2
Curve Equation t Generators 88110cm1 [1,-1,1,-39947,-3058729] 2 [120057:1680328:343] 88110cm2 [1,-1,1,-638897,-196399789] 2 [2713482954:-77044317029:2000376] 88110cm3 [1,-1,1,-165182,22926989] 6 [517:8431:1] 88110cm4 [1,-1,1,-660182,-182597011] 6 [967:8601:1]
88110cn (2 curves)	1	2- 3- 5- 11+ 89-	2- 3- 5- -2 11+ -6  6 -2
Curve Equation t Generators 88110cn1 [1,-1,1,-15872,-550429] 2 [-101:171:1] 88110cn2 [1,-1,1,-233672,-43413469] 2 [-281:171:1]
88110co (1 curve)	1	2- 3- 5- 11+ 89-	2- 3- 5- -4 11+  1 -2  3
Curve Equation t Generators 88110co1 [1,-1,1,463,66561] 1 [11:-276:1]
88110cp (1 curve)	1	2- 3- 5- 11- 89+	2- 3- 5-  2 11- -1  3  0
Curve Equation t Generators 88110cp1 [1,-1,1,-21632,2672291] 1 [189:2209:1]
88110cq (1 curve)	1	2- 3- 5- 11- 89+	2- 3- 5- -2 11- -3 -3 -6
Curve Equation t Generators 88110cq1 [1,-1,1,-85150247,2533225841471] 1 [4461:1495144:1]
88110cr (1 curve)	1	2- 3- 5- 11- 89+	2- 3- 5-  3 11-  2 -3  4
Curve Equation t Generators 88110cr1 [1,-1,1,-4757,-94611] 1 [-33:176:1]
88110cs (1 curve)	1	2- 3- 5- 11- 89+	2- 3- 5- -4 11-  5  3  6
Curve Equation t Generators 88110cs1 [1,-1,1,-48812,-37698001] 1 [447:5221:1]
88110ct (1 curve)	1	2- 3- 5- 11- 89+	2- 3- 5- -5 11-  3  4 -3
Curve Equation t Generators 88110ct1 [1,-1,1,-723722,241776969] 1 [437:2751:1]
88110cu (1 curve)	2	2- 3- 5- 11- 89-	2- 3- 5- -3 11- -6 -8 -3
Curve Equation t Generators 88110cu1 [1,-1,1,-28382,4335981] 1 [-109:-2421:1]&[-199:1539:1]
88110cv (2 curves)	0	2- 3- 5- 11- 89-	2- 3- 5- -4 11- -4  2  4
Curve Equation t 88110cv1 [1,-1,1,-1022,-3031] 2 88110cv2 [1,-1,1,3928,-26791] 2

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