Cremona's table of elliptic curves

50778 = 2 · 3² · 7 · 13 · 31

Class	r	Atkin-Lehner	Eigenvalues
50778a (2 curves)	1	2+ 3+ 7+ 13+ 31+	2+ 3+  2 7+ -4 13+ -2 -4
Curve Equation t Generators 50778a1 [1,-1,0,-3066,59840] 2 [-22:352:1] 50778a2 [1,-1,0,-11436,-403858] 2 [-49:217:1]
50778b (2 curves)	1	2+ 3+ 7+ 13+ 31+	2+ 3+ -4 7+ -4 13+ -2 -4
Curve Equation t Generators 50778b1 [1,-1,0,-2410224,-1439635456] 2 [1808:9600:1] 50778b2 [1,-1,0,-2408064,-1442346256] 2 [4108:238732:1]
50778c (2 curves)	2	2+ 3+ 7- 13+ 31+	2+ 3+ -2 7- -2 13+ -6 -4
Curve Equation t Generators 50778c1 [1,-1,0,-1218,16660] 2 [-28:182:1]&[-7:161:1] 50778c2 [1,-1,0,-978,23236] 2 [-36:122:1]&[15:-116:1]
50778d (2 curves)	0	2+ 3+ 7- 13- 31-	2+ 3+ -2 7-  4 13- -6 -4
Curve Equation t 50778d1 [1,-1,0,-35763,2599541] 2 50778d2 [1,-1,0,-571443,166410485] 2
50778e (1 curve)	1	2+ 3- 7+ 13+ 31-	2+ 3- -1 7+ -1 13+ -3  5
Curve Equation t Generators 50778e1 [1,-1,0,-18900,-1019336] 1 [1127:36962:1]
50778f (4 curves)	1	2+ 3- 7+ 13+ 31-	2+ 3- -2 7+  4 13+ -6  0
Curve Equation t Generators 50778f1 [1,-1,0,-22428,-85424] 2 [-91:1139:1] 50778f2 [1,-1,0,-255708,-49587440] 4 [-283:371:1] 50778f3 [1,-1,0,-155268,-89020184] 2 [92227533:-1608643235:132651] 50778f4 [1,-1,0,-4088628,-3181083080] 2 [176781:13430477:27]
50778g (1 curve)	0	2+ 3- 7+ 13- 31-	2+ 3-  1 7+ -1 13-  8  0
Curve Equation t 50778g1 [1,-1,0,-49824,-4451328] 1
50778h (1 curve)	1	2+ 3- 7- 13+ 31+	2+ 3-  1 7- -5 13+  0 -4
Curve Equation t Generators 50778h1 [1,-1,0,-10494,-422924] 1 [131:596:1]
50778i (4 curves)	1	2+ 3- 7- 13+ 31+	2+ 3-  2 7-  0 13+  2 -4
Curve Equation t Generators 50778i1 [1,-1,0,6489,-93443] 2 [21:217:1] 50778i2 [1,-1,0,-28791,-763763] 4 [-118:1049:1] 50778i3 [1,-1,0,-241731,45273865] 2 [-412:8855:1] 50778i4 [1,-1,0,-380331,-90125231] 2 [-44045:-5054:125]
50778j (2 curves)	0	2+ 3- 7- 13+ 31-	2+ 3-  0 7-  2 13+ -2  0
Curve Equation t 50778j1 [1,-1,0,-16323102,-25368128748] 2 50778j2 [1,-1,0,-13523742,-34352394732] 2
50778k (2 curves)	0	2+ 3- 7- 13+ 31-	2+ 3-  0 7- -4 13+  6  8
Curve Equation t 50778k1 [1,-1,0,-3402,60340] 2 50778k2 [1,-1,0,7758,366124] 2
50778l (1 curve)	0	2+ 3- 7- 13+ 31-	2+ 3-  3 7- -1 13+  4  6
Curve Equation t 50778l1 [1,-1,0,-4979763,4461016437] 1
50778m (2 curves)	0	2+ 3- 7- 13+ 31-	2+ 3-  4 7- -2 13+  6  0
Curve Equation t 50778m1 [1,-1,0,-5580,120528] 2 50778m2 [1,-1,0,13860,762048] 2
50778n (1 curve)	0	2+ 3- 7- 13- 31+	2+ 3-  3 7- -1 13- -7  1
Curve Equation t 50778n1 [1,-1,0,-1327653,589148437] 1
50778o (2 curves)	1	2+ 3- 7- 13- 31-	2+ 3-  0 7- -4 13-  2  4
Curve Equation t Generators 50778o1 [1,-1,0,-2322,-41472] 2 [-27:45:1] 50778o2 [1,-1,0,468,-136890] 2 [117:1170:1]
50778p (1 curve)	1	2+ 3- 7- 13- 31-	2+ 3-  1 7- -1 13- -7  1
Curve Equation t Generators 50778p1 [1,-1,0,-9234909,12600348421] 1 [3641:163208:1]
50778q (4 curves)	1	2+ 3- 7- 13- 31-	2+ 3-  2 7-  0 13- -2 -4
Curve Equation t Generators 50778q1 [1,-1,0,819,29029] 2 [3:176:1] 50778q2 [1,-1,0,-10701,390757] 4 [-43:899:1] 50778q3 [1,-1,0,-38781,-2501483] 2 [-93:589:1] 50778q4 [1,-1,0,-166941,26295349] 2 [110:2987:1]
50778r (2 curves)	1	2+ 3- 7- 13- 31-	2+ 3- -2 7-  2 13-  2 -2
Curve Equation t Generators 50778r1 [1,-1,0,-288,-1076] 2 [-10:32:1] 50778r2 [1,-1,0,882,-8330] 2 [29:188:1]
50778s (2 curves)	0	2- 3+ 7+ 13+ 31+	2- 3+ -2 7+  4 13+  2 -4
Curve Equation t 50778s1 [1,-1,1,-341,-2103] 2 50778s2 [1,-1,1,-1271,15381] 2
50778t (2 curves)	0	2- 3+ 7+ 13+ 31+	2- 3+  4 7+  4 13+  2 -4
Curve Equation t 50778t1 [1,-1,1,-267803,53409099] 2 50778t2 [1,-1,1,-267563,53509419] 2
50778u (2 curves)	1	2- 3+ 7- 13+ 31+	2- 3+  2 7-  2 13+  6 -4
Curve Equation t Generators 50778u1 [1,-1,1,-10964,-438857] 2 [197:2141:1] 50778u2 [1,-1,1,-8804,-618569] 2 [173:1649:1]
50778v (2 curves)	1	2- 3+ 7- 13- 31-	2- 3+  2 7- -4 13-  6 -4
Curve Equation t Generators 50778v1 [1,-1,1,-3974,-94955] 2 [-35:35:1] 50778v2 [1,-1,1,-63494,-6142187] 2 [469:7955:1]
50778w (1 curve)	1	2- 3- 7+ 13+ 31+	2- 3-  1 7+ -2 13+  2  2
Curve Equation t Generators 50778w1 [1,-1,1,283,-1713] 1 [4872:18901:512]
50778x (2 curves)	1	2- 3- 7+ 13+ 31+	2- 3- -2 7+ -2 13+  2  2
Curve Equation t Generators 50778x1 [1,-1,1,-1054415471,13177706665335] 2 [2526055:-44933106:125] 50778x2 [1,-1,1,-977738351,15175513691511] 2 [1326055:-306773106:125]
50778y (2 curves)	1	2- 3- 7+ 13+ 31+	2- 3- -2 7+ -2 13+  2 -4
Curve Equation t Generators 50778y1 [1,-1,1,-6206,7485] 2 [-1:117:1] 50778y2 [1,-1,1,-69386,7033101] 2 [161:45:1]
50778z (2 curves)	1	2- 3- 7+ 13+ 31+	2- 3- -2 7+  4 13+ -4 -4
Curve Equation t Generators 50778z1 [1,-1,1,-31946,-2419959] 2 [281:3135:1] 50778z2 [1,-1,1,-525866,-146644599] 2 [1653:58323:1]
50778ba (1 curve)	1	2- 3- 7+ 13+ 31+	2- 3- -3 7+  2 13+ -2 -6
Curve Equation t Generators 50778ba1 [1,-1,1,-1199,-119681] 1 [1877:80350:1]
50778bb (2 curves)	1	2- 3- 7+ 13+ 31+	2- 3- -4 7+  6 13+ -2 -2
Curve Equation t Generators 50778bb1 [1,-1,1,-48227,3667295] 2 [63:904:1] 50778bb2 [1,-1,1,-185117,-26722285] 2 [-14220:125131:64]
50778bc (1 curve)	0	2- 3- 7+ 13- 31+	2- 3-  1 7+  6 13-  6  2
Curve Equation t 50778bc1 [1,-1,1,-29642,3350153] 1
50778bd (4 curves)	0	2- 3- 7+ 13- 31+	2- 3- -2 7+  0 13- -6 -4
Curve Equation t 50778bd1 [1,-1,1,-72877586,239481583121] 4 50778bd2 [1,-1,1,-72878306,239476615121] 4 50778bd3 [1,-1,1,-69335366,263803858337] 2 50778bd4 [1,-1,1,-76432766,214831411265] 2
50778be (1 curve)	0	2- 3- 7+ 13- 31+	2- 3-  3 7+  5 13-  4  6
Curve Equation t 50778be1 [1,-1,1,-1147766,-473102971] 1
50778bf (2 curves)	1	2- 3- 7+ 13- 31-	2- 3-  0 7+  0 13- -2  6
Curve Equation t Generators 50778bf1 [1,-1,1,-780035,-157377981] 2 [-693:7418:1] 50778bf2 [1,-1,1,-11015195,-14064913389] 2 [-123084:179507:64]
50778bg (2 curves)	1	2- 3- 7+ 13- 31-	2- 3-  0 7+  0 13-  6  2
Curve Equation t Generators 50778bg1 [1,-1,1,-3785,-85431] 2 [-37:72:1] 50778bg2 [1,-1,1,-59945,-5634039] 2 [-141:72:1]
50778bh (2 curves)	1	2- 3- 7+ 13- 31-	2- 3- -2 7+ -2 13- -2 -2
Curve Equation t Generators 50778bh1 [1,-1,1,-1871006,983558445] 2 [1073:-15045:1] 50778bh2 [1,-1,1,-1197086,1701148461] 2 [641:-34917:1]
50778bi (1 curve)	1	2- 3- 7+ 13- 31-	2- 3-  3 7+ -3 13-  1  3
Curve Equation t Generators 50778bi1 [1,-1,1,409,-14817] 1 [107:1062:1]
50778bj (1 curve)	1	2- 3- 7+ 13- 31-	2- 3- -3 7+ -3 13-  0 -4
Curve Equation t Generators 50778bj1 [1,-1,1,187141,-82527303] 1 [2422:9549:8]
50778bk (2 curves)	1	2- 3- 7+ 13- 31-	2- 3- -4 7+ -2 13- -6 -2
Curve Equation t Generators 50778bk1 [1,-1,1,-146057,21501065] 2 [183:-1028:1] 50778bk2 [1,-1,1,-2336297,1375069385] 2 [885:-560:1]
50778bl (2 curves)	0	2- 3- 7- 13+ 31+	2- 3-  0 7- -4 13+ -2  8
Curve Equation t 50778bl1 [1,-1,1,-38945,-2948255] 2 50778bl2 [1,-1,1,-36605,-3319847] 2
50778bm (2 curves)	0	2- 3- 7- 13+ 31+	2- 3-  4 7-  4 13+  2 -2
Curve Equation t 50778bm1 [1,-1,1,-2228,-38541] 2 50778bm2 [1,-1,1,-5738,115899] 2
50778bn (1 curve)	1	2- 3- 7- 13+ 31-	2- 3- -1 7-  2 13+  6  6
Curve Equation t Generators 50778bn1 [1,-1,1,-1643,26075] 1 [25:0:1]
50778bo (1 curve)	1	2- 3- 7- 13+ 31-	2- 3- -1 7- -3 13+ -4  6
Curve Equation t Generators 50778bo1 [1,-1,1,14899342,-1546871727] 1 [27839:4675233:1]
50778bp (2 curves)	1	2- 3- 7- 13+ 31-	2- 3-  2 7-  0 13+  2 -6
Curve Equation t Generators 50778bp1 [1,-1,1,-36059,2574951] 2 [383:6504:1] 50778bp2 [1,-1,1,9571,8616363] 2 [222:23755:8]
50778bq (1 curve)	1	2- 3- 7- 13+ 31-	2- 3- -3 7-  5 13+ -3 -1
Curve Equation t Generators 50778bq1 [1,-1,1,-15834614,-56085871611] 1 [11561:-1148565:1]
50778br (2 curves)	1	2- 3- 7- 13+ 31-	2- 3- -4 7- -4 13+ -6  0
Curve Equation t Generators 50778br1 [1,-1,1,-915647,271532135] 2 [-429:-23978:1] 50778br2 [1,-1,1,1941313,1625731175] 2 [2667:-161858:1]
50778bs (2 curves)	1	2- 3- 7- 13- 31+	2- 3-  0 7-  2 13- -2  4
Curve Equation t Generators 50778bs1 [1,-1,1,-1014620,360078495] 2 [245:11109:1] 50778bs2 [1,-1,1,1197220,1711955103] 2 [-571:29301:1]
50778bt (2 curves)	1	2- 3- 7- 13- 31+	2- 3-  0 7-  2 13- -2 -4
Curve Equation t Generators 50778bt1 [1,-1,1,-1159160,-480055701] 2 [-39916:20511:64] 50778bt2 [1,-1,1,-1115420,-517987029] 2 [2945:145947:1]
50778bu (2 curves)	1	2- 3- 7- 13- 31+	2- 3-  0 7- -2 13- -2  0
Curve Equation t Generators 50778bu1 [1,-1,1,-73355,805659] 2 [-223:2568:1] 50778bu2 [1,-1,1,291685,6208251] 2 [89:5688:1]
50778bv (2 curves)	1	2- 3- 7- 13- 31+	2- 3-  2 7-  2 13-  6 -4
Curve Equation t Generators 50778bv1 [1,-1,1,-509,3381] 2 [-7:84:1] 50778bv2 [1,-1,1,-7529,253293] 2 [71:234:1]
50778bw (4 curves)	1	2- 3- 7- 13- 31+	2- 3- -2 7-  0 13- -6  4
Curve Equation t Generators 50778bw1 [1,-1,1,-11876,494471] 4 [-123:349:1] 50778bw2 [1,-1,1,-23396,-611449] 4 [351:-6035:1] 50778bw3 [1,-1,1,82444,-4675705] 2 [295:-6875:1] 50778bw4 [1,-1,1,-313556,-67464313] 2 [-317:207:1]
50778bx (1 curve)	1	2- 3- 7- 13- 31+	2- 3- -3 7- -1 13-  4 -4
Curve Equation t Generators 50778bx1 [1,-1,1,121,-1281] 1 [11:30:1]
50778by (6 curves)	0	2- 3- 7- 13- 31-	2- 3-  0 7-  0 13-  6  2
Curve Equation t 50778by1 [1,-1,1,-1535315,-731775121] 2 50778by2 [1,-1,1,-24564425,-46854476629] 2 50778by3 [1,-1,1,-3339590,1279394453] 6 50778by4 [1,-1,1,-24694430,-46333356811] 6 50778by5 [1,-1,1,-234615245,1383250308725] 6 50778by6 [1,-1,1,-235513805,1372121463413] 6
50778bz (3 curves)	0	2- 3- 7- 13- 31-	2- 3-  3 7-  3 13-  0  2
Curve Equation t 50778bz1 [1,-1,1,-17726,-904021] 1 50778bz2 [1,-1,1,2929,-2860657] 3 50778bz3 [1,-1,1,-26366,77255309] 3
50778ca (2 curves)	2	2- 3- 7- 13- 31-	2- 3- -4 7- -4 13- -6 -4
Curve Equation t Generators 50778ca1 [1,-1,1,-87707,9520075] 2 [763:-20038:1]&[-277:3674:1] 50778ca2 [1,-1,1,62053,38573515] 2 [211:-7918:1]&[-223:3800:1]

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