Cremona's table of elliptic curves

51984 = 2⁴ · 3² · 19²

Class	r	Atkin-Lehner	Eigenvalues
51984a (1 curve)	1	2+ 3+ 19+	2+ 3+  2 -3  6 -1  2 19+
Curve Equation t Generators 51984a1 [0,0,0,-555579,161858682] 1 [361:2888:1]
51984b (1 curve)	1	2+ 3+ 19+	2+ 3+ -2 -3 -6 -1 -2 19+
Curve Equation t Generators 51984b1 [0,0,0,-61731,-5994766] 1 [361:4332:1]
51984c (2 curves)	0	2+ 3+ 19-	2+ 3+  0  0  2  2 -4 19-
Curve Equation t 51984c1 [0,0,0,-5415,-96026] 2 51984c2 [0,0,0,16245,-672182] 2
51984d (2 curves)	0	2+ 3+ 19-	2+ 3+  0  0 -2  2  4 19-
Curve Equation t 51984d1 [0,0,0,-48735,2592702] 2 51984d2 [0,0,0,146205,18148914] 2
51984e (1 curve)	0	2+ 3+ 19-	2+ 3+  2 -3  6  1  2 19-
Curve Equation t 51984e1 [0,0,0,-1539,-23598] 1
51984f (1 curve)	2	2+ 3+ 19-	2+ 3+ -2 -3 -6  1 -2 19-
Curve Equation t Generators 51984f1 [0,0,0,-171,874] 1 [5:-12:1]&[-13:30:1]
51984g (2 curves)	0	2+ 3+ 19-	2+ 3+  4  0  6 -2  4 19-
Curve Equation t 51984g1 [0,0,0,-6498,-240065] 2 51984g2 [0,0,0,-109383,-13923770] 2
51984h (2 curves)	0	2+ 3+ 19-	2+ 3+ -4  0 -6 -2 -4 19-
Curve Equation t 51984h1 [0,0,0,-58482,6481755] 2 51984h2 [0,0,0,-984447,375941790] 2
51984i (1 curve)	0	2+ 3- 19+	2+ 3-  0 -3  2  1 -4 19+
Curve Equation t 51984i1 [0,0,0,-205770,-36098917] 1
51984j (2 curves)	0	2+ 3- 19+	2+ 3-  2  4  2  0  2 19+
Curve Equation t 51984j1 [0,0,0,-399,-722] 2 51984j2 [0,0,0,-3819,90250] 2
51984k (2 curves)	0	2+ 3- 19+	2+ 3-  2  4  2  0  2 19+
Curve Equation t 51984k1 [0,0,0,-144039,4952198] 2 51984k2 [0,0,0,-1378659,-619024750] 2
51984l (1 curve)	0	2+ 3- 19+	2+ 3-  2  5 -4  5  0 19+
Curve Equation t 51984l1 [0,0,0,-144039,-47176202] 1
51984m (1 curve)	0	2+ 3- 19+	2+ 3- -2  3  0  5  4 19+
Curve Equation t 51984m1 [0,0,0,41154,1433531] 1
51984n (1 curve)	0	2+ 3- 19+	2+ 3- -3  0 -4 -5  5 19+
Curve Equation t 51984n1 [0,0,0,-1378659,623064701] 1
51984o (1 curve)	0	2+ 3- 19+	2+ 3- -3 -1 -3  0  7 19+
Curve Equation t 51984o1 [0,0,0,-37164,11625644] 1
51984p (1 curve)	0	2+ 3- 19+	2+ 3- -3 -1 -3  0  7 19+
Curve Equation t 51984p1 [0,0,0,-13416204,-79740292196] 1
51984q (1 curve)	0	2+ 3- 19+	2+ 3-  4  0  3  2 -2 19+
Curve Equation t 51984q1 [0,0,0,-1083,-25270] 1
51984r (1 curve)	1	2+ 3- 19-	2+ 3-  0 -3  2 -1 -4 19-
Curve Equation t Generators 51984r1 [0,0,0,-570,5263] 1 [11:18:1]
51984s (1 curve)	1	2+ 3- 19-	2+ 3-  0 -3  2 -1  5 19-
Curve Equation t Generators 51984s1 [0,0,0,-27075,2455522] 1 [-171:1444:1]
51984t (1 curve)	1	2+ 3- 19-	2+ 3-  1  3 -3  4 -5 19-
Curve Equation t Generators 51984t1 [0,0,0,-4332,-631028] 1 [1778761:33052077:4913]
51984u (1 curve)	1	2+ 3- 19-	2+ 3- -1  3 -5  2  1 19-
Curve Equation t Generators 51984u1 [0,0,0,177612,-20604436] 1 [49609:11049849:1]
51984v (6 curves)	1	2+ 3- 19-	2+ 3-  2  0  4  2 -2 19-
Curve Equation t Generators 51984v1 [0,0,0,2166,-48013] 2 [32053:337896:343] 51984v2 [0,0,0,-14079,-480130] 4 [-205790:284760:2197] 51984v3 [0,0,0,-79059,8162210] 4 [-317:1170:1] 51984v4 [0,0,0,-209019,-36777958] 2 [-842195366194:99089194680:3170044709] 51984v5 [0,0,0,50901,32360762] 2 [209:7220:1] 51984v6 [0,0,0,-1248699,537073418] 2 [38671:7601490:1]
51984w (1 curve)	1	2+ 3- 19-	2+ 3-  2  5 -4 -5  0 19-
Curve Equation t Generators 51984w1 [0,0,0,-399,6878] 1 [49:324:1]
51984x (4 curves)	1	2+ 3- 19-	2+ 3- -2  0  0 -2 -2 19-
Curve Equation t Generators 51984x1 [0,0,0,-559911,161227654] 2 [389:1512:1] 51984x2 [0,0,0,-624891,121472890] 4 [946:56133:8] 51984x3 [0,0,0,1844349,843972514] 2 [2375:136458:1] 51984x4 [0,0,0,-4133811,-3145331630] 2 [-251706:-2042425:216]
51984y (1 curve)	1	2+ 3- 19-	2+ 3- -2  3  0 -5  4 19-
Curve Equation t Generators 51984y1 [0,0,0,114,-209] 1 [35:216:1]
51984z (1 curve)	1	2+ 3- 19-	2+ 3-  3  3 -1  2  5 19-
Curve Equation t Generators 51984z1 [0,0,0,-186276,-35200388] 1 [18764039:4388628987:343]
51984ba (1 curve)	1	2+ 3- 19-	2+ 3- -3  0 -4  5  5 19-
Curve Equation t Generators 51984ba1 [0,0,0,-3819,-90839] 1 [-1062432:4739:29791]
51984bb (1 curve)	1	2+ 3- 19-	2+ 3-  4  0  3 -2 -2 19-
Curve Equation t Generators 51984bb1 [0,0,0,-390963,173326930] 1 [4773875122515:191940766265530:2679826869]
51984bc (2 curves)	1	2+ 3- 19-	2+ 3- -4 -4 -4  4 -6 19-
Curve Equation t Generators 51984bc1 [0,0,0,-53067,-4183990] 2 [589:-12996:1] 51984bc2 [0,0,0,76893,-21468670] 2 [551:-13718:1]
51984bd (2 curves)	0	2- 3+ 19+	2- 3+  0  1  0 -7  0 19+
Curve Equation t 51984bd1 [0,0,0,0,-130321] 1 51984bd2 [0,0,0,0,3518667] 1
51984be (2 curves)	0	2- 3+ 19+	2- 3+  0 -5  0  5  0 19+
Curve Equation t 51984be1 [0,0,0,0,-361] 1 51984be2 [0,0,0,0,9747] 1
51984bf (2 curves)	0	2- 3+ 19+	2- 3+  2  0 -4  6 -4 19+
Curve Equation t 51984bf1 [0,0,0,-22059,1228122] 2 51984bf2 [0,0,0,-350379,79827930] 2
51984bg (2 curves)	0	2- 3+ 19+	2- 3+  2  0 -4 -6 -4 19+
Curve Equation t 51984bg1 [0,0,0,-7963299,-8423688798] 2 51984bg2 [0,0,0,-126486819,-547539771870] 2
51984bh (1 curve)	0	2- 3+ 19+	2- 3+  2 -3 -2 -1  6 19+
Curve Equation t 51984bh1 [0,0,0,-555579,-1808594838] 1
51984bi (2 curves)	0	2- 3+ 19+	2- 3+ -2  0  4  6  4 19+
Curve Equation t 51984bi1 [0,0,0,-2451,-45486] 2 51984bi2 [0,0,0,-38931,-2956590] 2
51984bj (2 curves)	0	2- 3+ 19+	2- 3+ -2  0  4 -6  4 19+
Curve Equation t 51984bj1 [0,0,0,-884811,311988474] 2 51984bj2 [0,0,0,-14054091,20279250810] 2
51984bk (1 curve)	2	2- 3+ 19+	2- 3+ -2 -3  2 -1 -6 19+
Curve Equation t Generators 51984bk1 [0,0,0,-61731,66984994] 1 [3249:-184832:1]&[-241:8238:1]
51984bl (1 curve)	0	2- 3+ 19+	2- 3+  4  3 -4  5  0 19+
Curve Equation t 51984bl1 [0,0,0,-493848,-133579025] 1
51984bm (1 curve)	0	2- 3+ 19+	2- 3+ -4  3  4  5  0 19+
Curve Equation t 51984bm1 [0,0,0,-4444632,3606633675] 1
51984bn (2 curves)	1	2- 3+ 19-	2- 3+  0  1  0  7  0 19-
Curve Equation t Generators 51984bn1 [0,0,0,0,19] 1 [5:12:1] 51984bn2 [0,0,0,0,-513] 1 [1005:324:125]
51984bo (4 curves)	1	2- 3+ 19-	2- 3+  0  4  0 -2  0 19-
Curve Equation t Generators 51984bo1 [0,0,0,0,6859] 2 [4484:37905:64] 51984bo2 [0,0,0,-5415,150898] 2 [4634:97140:343] 51984bo3 [0,0,0,0,-185193] 2 [52814205:1270868732:91125] 51984bo4 [0,0,0,-48735,-4074246] 2 [716543881993980:16108409487404017:1197770328000]
51984bp (2 curves)	1	2- 3+ 19-	2- 3+  0 -5  0 -5  0 19-
Curve Equation t Generators 51984bp1 [0,0,0,0,2476099] 1 [-127:654:1] 51984bp2 [0,0,0,0,-66854673] 1 [997713651:14294592450:2048383]
51984bq (2 curves)	1	2- 3+ 19-	2- 3+  2  0 -2  4  0 19-
Curve Equation t Generators 51984bq1 [0,0,0,-165699,-2592702] 2 [-17205:524502:125] 51984bq2 [0,0,0,-1725219,868555170] 2 [3097:158840:1]
51984br (1 curve)	1	2- 3+ 19-	2- 3+  2 -3 -2  1  6 19-
Curve Equation t Generators 51984br1 [0,0,0,-1539,263682] 1 [1:512:1]
51984bs (2 curves)	1	2- 3+ 19-	2- 3+ -2  0  2  4  0 19-
Curve Equation t Generators 51984bs1 [0,0,0,-18411,96026] 2 [5:64:1] 51984bs2 [0,0,0,-191691,-32168710] 2 [-2126:571:8]
51984bt (1 curve)	1	2- 3+ 19-	2- 3+ -2 -3  2  1 -6 19-
Curve Equation t Generators 51984bt1 [0,0,0,-171,-9766] 1 [85:768:1]
51984bu (1 curve)	1	2- 3+ 19-	2- 3+  4  3 -4 -5  0 19-
Curve Equation t Generators 51984bu1 [0,0,0,-1368,19475] 1 [25:30:1]
51984bv (1 curve)	1	2- 3+ 19-	2- 3+ -4  3  4 -5  0 19-
Curve Equation t Generators 51984bv1 [0,0,0,-12312,-525825] 1 [4251219:473266422:343]
51984bw (1 curve)	1	2- 3- 19+	2- 3-  0 -1 -2 -3 -4 19+
Curve Equation t Generators 51984bw1 [0,0,0,-157035,25094554] 1 [245:1152:1]
51984bx (2 curves)	1	2- 3- 19+	2- 3-  0 -1 -2  5  4 19+
Curve Equation t Generators 51984bx1 [0,0,0,102885,13814026] 1 [1805:77976:1] 51984bx2 [0,0,0,-34466475,-77884781798] 1 [23083423:2836221048:1331]
51984by (2 curves)	1	2- 3- 19+	2- 3-  0  4  3  2  6 19+
Curve Equation t Generators 51984by1 [0,0,0,102885,-27888694] 1 [13547380647723023:392633169490060342:18003268247329] 51984by2 [0,0,0,-4835595,-4100159302] 1 [207658313245787645974192138729104673861618480350493:-12361081626448388778395258066513738250480936180092614:43766802600094490461249068077239086213731857883]
51984bz (1 curve)	1	2- 3- 19+	2- 3-  1  0 -4 -1 -3 19+
Curve Equation t Generators 51984bz1 [0,0,0,-20577,912247] 1 [-2166:38627:27]
51984ca (1 curve)	1	2- 3- 19+	2- 3-  1 -1  1  4  3 19+
Curve Equation t Generators 51984ca1 [0,0,0,-329232,128757148] 1 [-15162:315514:27]
51984cb (1 curve)	1	2- 3- 19+	2- 3-  1 -1  1 -4  3 19+
Curve Equation t Generators 51984cb1 [0,0,0,-912,-18772] 1 [38:38:1]
51984cc (2 curves)	1	2- 3- 19+	2- 3-  1 -3 -5  0  7 19+
Curve Equation t Generators 51984cc1 [0,0,0,-5472,155952] 1 [57:171:1] 51984cc2 [0,0,0,-1975392,-1069674768] 1 [576225976893771:2664196565893983:352943569763]
51984cd (1 curve)	1	2- 3- 19+	2- 3- -2  3 -2  3  1 19+
Curve Equation t Generators 51984cd1 [0,0,0,-171,-19494] 1 [133:1520:1]
51984ce (1 curve)	1	2- 3- 19+	2- 3- -2  3 -2 -3  1 19+
Curve Equation t Generators 51984ce1 [0,0,0,-61731,133709346] 1 [-1135345:57217778:4913]
51984cf (2 curves)	1	2- 3- 19+	2- 3- -2 -4 -2  4 -6 19+
Curve Equation t Generators 51984cf1 [0,0,0,-139251,-19325774] 2 [-241:486:1] 51984cf2 [0,0,0,-358131,56362930] 2 [551:5130:1]
51984cg (2 curves)	1	2- 3- 19+	2- 3- -2 -4 -2 -4 -6 19+
Curve Equation t Generators 51984cg1 [0,0,0,-50269611,132555483866] 2 [-1579:456064:1] 51984cg2 [0,0,0,-129285291,-386593336870] 2 [-1405831:-93587794:343]
51984ch (1 curve)	1	2- 3- 19+	2- 3-  4  3  2 -7  0 19+
Curve Equation t Generators 51984ch1 [0,0,0,4547517,-4799722430] 1 [416955:52272800:27]
51984ci (3 curves)	0	2- 3- 19-	2- 3-  0  1 -6 -5 -3 19-
Curve Equation t 51984ci1 [0,0,0,-806835,-279037838] 1 51984ci2 [0,0,0,492765,-1060305374] 1 51984ci3 [0,0,0,-4445715,29021951698] 1
51984cj (1 curve)	0	2- 3- 19-	2- 3-  0 -1 -2  3 -4 19-
Curve Equation t 51984cj1 [0,0,0,-56689635,-172123545886] 1
51984ck (2 curves)	2	2- 3- 19-	2- 3-  0 -1 -2 -5  4 19-
Curve Equation t Generators 51984ck1 [0,0,0,285,-2014] 1 [7:18:1]&[17:88:1] 51984ck2 [0,0,0,-95475,11355122] 1 [-287:3888:1]&[137:920:1]
51984cl (4 curves)	0	2- 3- 19-	2- 3-  0  4  0  4 -6 19-
Curve Equation t 51984cl1 [0,0,0,-416955,-7915286] 2 51984cl2 [0,0,0,1662405,-63226262] 2 51984cl3 [0,0,0,-22250235,40396752682] 2 51984cl4 [0,0,0,-21730395,42374120074] 2
51984cm (2 curves)	0	2- 3- 19-	2- 3-  0  4  3 -2  6 19-
Curve Equation t 51984cm1 [0,0,0,285,4066] 1 51984cm2 [0,0,0,-13395,597778] 1
51984cn (2 curves)	0	2- 3- 19-	2- 3-  0 -4  4  0  2 19-
Curve Equation t 51984cn1 [0,0,0,-4965555,4258218098] 2 51984cn2 [0,0,0,-4445715,5184676946] 2
51984co (1 curve)	0	2- 3- 19-	2- 3-  1  0 -4  1 -3 19-
Curve Equation t 51984co1 [0,0,0,-57,-133] 1
51984cp (1 curve)	0	2- 3- 19-	2- 3-  1  3  5  4  3 19-
Curve Equation t 51984cp1 [0,0,0,-69312,7051052] 1
51984cq (2 curves)	0	2- 3- 19-	2- 3- -1 -3 -3  6 -3 19-
Curve Equation t 51984cq1 [0,0,0,1022352,454449904] 1 51984cq2 [0,0,0,-228227088,1327088209264] 1
51984cr (4 curves)	0	2- 3- 19-	2- 3-  2  0  0 -6  6 19-
Curve Equation t 51984cr1 [0,0,0,-79059,7394002] 2 51984cr2 [0,0,0,-338979,-68658590] 4 51984cr3 [0,0,0,440781,-338299598] 2 51984cr4 [0,0,0,-5277459,-4666383470] 2
51984cs (2 curves)	0	2- 3- 19-	2- 3- -2  0  2 -2 -6 19-
Curve Equation t 51984cs1 [0,0,0,8664,-3504949] 2 51984cs2 [0,0,0,-299991,-60976510] 2
51984ct (4 curves)	0	2- 3- 19-	2- 3- -2  0 -4 -2  6 19-
Curve Equation t 51984ct1 [0,0,0,-18299451,27072514154] 2 51984ct2 [0,0,0,-284457531,1846582380650] 4 51984ct3 [0,0,0,-276140091,1959638015594] 2 51984ct4 [0,0,0,-4551304251,118182158201450] 4
51984cu (1 curve)	0	2- 3- 19-	2- 3-  3 -1 -5  6  5 19-
Curve Equation t 51984cu1 [0,0,0,8664,-1838212] 1
51984cv (1 curve)	0	2- 3- 19-	2- 3-  3  5  1 -2  1 19-
Curve Equation t 51984cv1 [0,0,0,-121296,-17888272] 1
51984cw (3 curves)	0	2- 3- 19-	2- 3- -3  1  3  4  3 19-
Curve Equation t 51984cw1 [0,0,0,34656,109744] 1 51984cw2 [0,0,0,-485184,138387184] 1 51984cw3 [0,0,0,-39993024,97347427504] 1
51984cx (1 curve)	0	2- 3- 19-	2- 3-  4  3  2  7  0 19-
Curve Equation t 51984cx1 [0,0,0,12597,699770] 1
51984cy (2 curves)	0	2- 3- 19-	2- 3-  4 -3  2  1 -3 19-
Curve Equation t 51984cy1 [0,0,0,-1083,-14060950] 1 51984cy2 [0,0,0,-3639963,2958904010] 1

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