Cremona's table of elliptic curves

68355 = 3² · 5 · 7² · 31

Class	r	Atkin-Lehner	Eigenvalues
68355a (1 curve)	2	3+ 5+ 7+ 31-	0 3+ 5+ 7+ -3 -4 -7  7
Curve Equation t Generators 68355a1 [0,0,1,-2058,31813] 1 [-49:122:1]&[1:172:1]
68355b (1 curve)	0	3+ 5+ 7+ 31-	-2 3+ 5+ 7+  5 -2  3  7
Curve Equation t 68355b1 [0,0,1,-110103,-13905992] 1
68355c (1 curve)	2	3+ 5+ 7- 31+	0 3+ 5+ 7-  3  4 -7 -7
Curve Equation t Generators 68355c1 [0,0,1,-378,2504] 1 [-6:67:1]&[4:32:1]
68355d (1 curve)	0	3+ 5+ 7- 31+	2 3+ 5+ 7- -5  2  3 -7
Curve Equation t 68355d1 [0,0,1,-20223,-1094641] 1
68355e (1 curve)	1	3+ 5- 7+ 31-	0 3+ 5- 7+  3 -4  7  7
Curve Equation t Generators 68355e1 [0,0,1,-18522,-858958] 1 [-98:122:1]
68355f (1 curve)	1	3+ 5- 7+ 31-	2 3+ 5- 7+ -5 -2 -3  7
Curve Equation t Generators 68355f1 [0,0,1,-990927,375461777] 1 [5826:50621:8]
68355g (1 curve)	1	3+ 5- 7- 31+	0 3+ 5- 7- -3  4  7 -7
Curve Equation t Generators 68355g1 [0,0,1,-42,-93] 1 [-3:2:1]
68355h (1 curve)	1	3+ 5- 7- 31+	-2 3+ 5- 7-  5  2 -3 -7
Curve Equation t Generators 68355h1 [0,0,1,-2247,40542] 1 [32:-38:1]
68355i (1 curve)	0	3- 5+ 7+ 31+	1 3- 5+ 7+  2 -6  4  4
Curve Equation t 68355i1 [1,-1,0,771300,314398125] 1
68355j (2 curves)	1	3- 5+ 7- 31+	0 3- 5+ 7- -3  4 -3  1
Curve Equation t Generators 68355j1 [0,0,1,-1627878,632023033] 1 [401:6612:1] 68355j2 [0,0,1,-41820618,-104043939386] 1 [-3400956441626:-6346544257118:915498611]
68355k (2 curves)	1	3- 5+ 7- 31+	1 3- 5+ 7-  2  2  2 -4
Curve Equation t Generators 68355k1 [1,-1,0,-4860,157891] 2 [30:181:1] 68355k2 [1,-1,0,-82035,9063886] 2 [-914:33379:8]
68355l (2 curves)	1	3- 5+ 7- 31+	1 3- 5+ 7-  4 -2  2 -8
Curve Equation t Generators 68355l1 [1,-1,0,-31148280,66919047075] 2 [102420:9260415:64] 68355l2 [1,-1,0,-31101975,67127891886] 2 [3062082412:-279910525581:1906624]
68355m (2 curves)	1	3- 5+ 7- 31+	1 3- 5+ 7- -4  0 -8 -4
Curve Equation t Generators 68355m1 [1,-1,0,-450,-12825] 2 [58:363:1] 68355m2 [1,-1,0,-11475,-469260] 2 [1094:5137:8]
68355n (4 curves)	1	3- 5+ 7- 31+	1 3- 5+ 7- -4  6 -2 -4
Curve Equation t Generators 68355n1 [1,-1,0,-2549430,-1557183825] 2 [22570:3370695:1] 68355n2 [1,-1,0,-4156875,644694336] 4 [-7850256:-8250225972:300763] 68355n3 [1,-1,0,16263630,5092280325] 2 [42950462661076308:11224475892352621527:102845289222208] 68355n4 [1,-1,0,-50296500,137098021311] 2 [858:307101:1]
68355o (1 curve)	1	3- 5+ 7- 31+	-1 3- 5+ 7-  2 -2  0  4
Curve Equation t Generators 68355o1 [1,-1,1,22,186] 1 [-4:6:1]
68355p (1 curve)	1	3- 5+ 7- 31+	-2 3- 5+ 7- -1  2  5  5
Curve Equation t Generators 68355p1 [0,0,1,-3423,-77072] 1 [-34:2:1]
68355q (1 curve)	0	3- 5+ 7- 31-	0 3- 5+ 7-  4  6  5  1
Curve Equation t 68355q1 [0,0,1,-588,7803] 1
68355r (1 curve)	0	3- 5+ 7- 31-	0 3- 5+ 7- -4  2 -1 -3
Curve Equation t 68355r1 [0,0,1,882,-1359052] 1
68355s (1 curve)	0	3- 5+ 7- 31-	0 3- 5+ 7- -4  2  3  5
Curve Equation t 68355s1 [0,0,1,5670672,6209546719] 1
68355t (2 curves)	2	3- 5- 7+ 31-	0 3- 5- 7+ -3 -4  3 -1
Curve Equation t Generators 68355t1 [0,0,1,-33222,-1842633] 1 [-1134:1081:8]&[-133:472:1] 68355t2 [0,0,1,-853482,303335100] 3 [1838:-70313:1]&[-952:15907:1]
68355u (1 curve)	0	3- 5- 7+ 31-	-1 3- 5- 7+  2  2  0 -4
Curve Equation t 68355u1 [1,-1,1,1093,-66076] 1
68355v (1 curve)	2	3- 5- 7+ 31-	-2 3- 5- 7+ -1 -2 -5 -5
Curve Equation t Generators 68355v1 [0,0,1,-167727,26435610] 1 [98:-3308:1]&[-52:5917:1]
68355w (4 curves)	0	3- 5- 7- 31+	1 3- 5- 7-  0 -2 -2  4
Curve Equation t 68355w1 [1,-1,0,-61749,-5258520] 2 68355w2 [1,-1,0,-240354,39857103] 4 68355w3 [1,-1,0,374841,210020040] 2 68355w4 [1,-1,0,-3713229,2754950778] 2
68355x (6 curves)	0	3- 5- 7- 31+	1 3- 5- 7- -4  2 -6 -4
Curve Equation t 68355x1 [1,-1,0,-8343729,9278677008] 2 68355x2 [1,-1,0,-8345934,9273529215] 4 68355x3 [1,-1,0,-6262209,14015670570] 2 68355x4 [1,-1,0,-10464939,4201902648] 4 68355x5 [1,-1,0,39365856,32635354275] 2 68355x6 [1,-1,0,-94199814,-348841077327] 2
68355y (2 curves)	0	3- 5- 7- 31+	-1 3- 5- 7- -2  0 -4 -4
Curve Equation t 68355y1 [1,-1,1,-31305497,-68922888856] 2 68355y2 [1,-1,1,-504002372,-4354959993856] 2
68355z (2 curves)	0	3- 5- 7- 31+	-1 3- 5- 7-  4  0  2  8
Curve Equation t 68355z1 [1,-1,1,-3317,177356] 2 68355z2 [1,-1,1,-71672,7395644] 2
68355ba (1 curve)	0	3- 5- 7- 31+	2 3- 5- 7-  1 -3  5  2
Curve Equation t 68355ba1 [0,0,1,-14681037,21651379965] 1
68355bb (2 curves)	0	3- 5- 7- 31+	2 3- 5- 7- -2  6 -7  5
Curve Equation t 68355bb1 [0,0,1,4263,88065] 1 68355bb2 [0,0,1,-370587,-86996205] 1
68355bc (1 curve)	0	3- 5- 7- 31+	-2 3- 5- 7-  5  5 -3  2
Curve Equation t 68355bc1 [0,0,1,-147,-81720] 1
68355bd (1 curve)	1	3- 5- 7- 31-	0 3- 5- 7- -1 -7 -7 -6
Curve Equation t Generators 68355bd1 [0,0,1,-366912,-86476903] 1 [1057:26582:1]
68355be (1 curve)	1	3- 5- 7- 31-	1 3- 5- 7-  2  6 -4 -4
Curve Equation t Generators 68355be1 [1,-1,0,15741,-921110] 1 [146:2042:1]
68355bf (2 curves)	1	3- 5- 7- 31-	1 3- 5- 7-  4  2 -2  8
Curve Equation t Generators 68355bf1 [1,-1,0,-635679,-194917640] 2 [3896:235652:1] 68355bf2 [1,-1,0,-634734,-195526787] 2 [1052:16799:1]
68355bg (4 curves)	1	3- 5- 7- 31-	1 3- 5- 7-  4 -2 -2 -4
Curve Equation t Generators 68355bg1 [1,-1,0,10281,-168400] 2 [1262:17891:8] 68355bg2 [1,-1,0,-44844,-1370125] 4 [11566:1237837:1] 68355bg3 [1,-1,0,-386619,91661030] 2 [740596:79182043:64] 68355bg4 [1,-1,0,-585069,-171973180] 2 [-2983774132:-20070571:6644672]
68355bh (4 curves)	1	3- 5- 7- 31-	1 3- 5- 7-  4 -2 -6  4
Curve Equation t Generators 68355bh1 [1,-1,0,-4419,-111560] 2 [45768:207073:512] 68355bh2 [1,-1,0,-6624,13243] 4 [-46:491:1] 68355bh3 [1,-1,0,26451,86008] 2 [5876:113009:64] 68355bh4 [1,-1,0,-74979,7901410] 2 [-166:4052:1]
68355bi (6 curves)	1	3- 5- 7- 31-	1 3- 5- 7- -4 -6  2 -4
Curve Equation t Generators 68355bi1 [1,-1,0,-288864,107560795] 2 [1634:62399:1] 68355bi2 [1,-1,0,-5583069,5076701608] 4 [-7418:781633:8] 68355bi3 [1,-1,0,-6555474,3187707655] 4 [-2194:84797:1] 68355bi4 [1,-1,0,-89317944,324927177133] 2 [66982:3206185:8] 68355bi5 [1,-1,0,22385151,23671882030] 4 [-402:1201451:8] 68355bi6 [1,-1,0,-51054579,-138203748572] 2 [208686:32174407:8]
68355bj (2 curves)	1	3- 5- 7- 31-	-1 3- 5- 7- -6  0 -4 -4
Curve Equation t Generators 68355bj1 [1,-1,1,1820218,-354602244] 2 [366:18804:1] 68355bj2 [1,-1,1,-7826657,-2928388494] 2 [-544:34449:1]
68355bk (1 curve)	1	3- 5- 7- 31-	-2 3- 5- 7-  1  1  1  2
Curve Equation t Generators 68355bk1 [0,0,1,-14979447,-38947086880] 1 [187761:11867174:27]

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