Cremona's table of elliptic curves

117670 = 2 · 5 · 7 · 41²

Class	r	Atkin-Lehner	Eigenvalues
117670a (4 curves)	1	2+ 5+ 7+ 41+	2+  2 5+ 7+  0 -2  0  4
Curve Equation t Generators 117670a1 [1,1,0,-118247458,494871618612] 2 [6321:2772:1] 117670a2 [1,1,0,-117911258,497825942492] 2 [130323:-5544023:27] 117670a3 [1,1,0,-133065473,362998246133] 2 [2997301430262:-40862018251771:1033364331] 117670a4 [1,1,0,404854527,2558034598133] 2 [528303518974562268:-1493436530583012514219:66135317184]
117670b (4 curves)	1	2+ 5+ 7+ 41+	2+  2 5+ 7+ -6  4  6 -2
Curve Equation t Generators 117670b1 [1,1,0,-168954823,845216166177] 2 [1369467408:-3714667079:185193] 117670b2 [1,1,0,-169375073,840799590827] 2 [755051402373555:10412321155937113:113731651125] 117670b3 [1,1,0,-188311538,639519274868] 2 [31123415371500554710:-7158472919741512274489:14457238157881000] 117670b4 [1,1,0,-1238936538,-16311894850132] 2 [-55764512033534175628153372598755953870:1920910117075948476544432930085673982733:2751138920167397637637043433843000]
117670c (1 curve)	0	2+ 5+ 7+ 41-	2+  0 5+ 7+ -3 -3  3 -2
Curve Equation t 117670c1 [1,-1,0,-1908250,1307303220] 1
117670d (1 curve)	0	2+ 5+ 7+ 41-	2+  0 5+ 7+  4  4  3  5
Curve Equation t 117670d1 [1,-1,0,1280711560,-107421508824994] 1
117670e (1 curve)	0	2+ 5+ 7- 41+	2+  0 5+ 7-  3  3 -3  2
Curve Equation t 117670e1 [1,-1,0,-1135,19245] 1
117670f (1 curve)	0	2+ 5+ 7- 41+	2+  0 5+ 7- -4 -4 -3 -5
Curve Equation t 117670f1 [1,-1,0,761875,-1558803789] 1
117670g (2 curves)	0	2+ 5+ 7- 41+	2+  0 5+ 7- -6  0  0  2
Curve Equation t 117670g1 [1,-1,0,-59150,-4656764] 2 117670g2 [1,-1,0,108950,-26408904] 2
117670h (2 curves)	0	2+ 5+ 7- 41+	2+  2 5+ 7-  4  2  4  8
Curve Equation t 117670h1 [1,1,0,-64753,6138657] 2 117670h2 [1,1,0,19297,21049127] 2
117670i (2 curves)	0	2+ 5- 7+ 41+	2+  2 5- 7+  0 -4 -2  4
Curve Equation t 117670i1 [1,1,0,-2597,-45619] 2 117670i2 [1,1,0,-10797,382421] 2
117670j (2 curves)	1	2+ 5- 7- 41+	2+ -2 5- 7-  0  4  2 -4
Curve Equation t Generators 117670j1 [1,0,1,-4366433,-3069882732] 2 [-893:11282:1] 117670j2 [1,0,1,-18150633,26665393508] 2 [2450448:-45189197:729]
117670k (2 curves)	2	2- 5+ 7+ 41+	2- -1 5+ 7+ -6  1  0  4
Curve Equation t Generators 117670k1 [1,1,1,129,229] 1 [-1:10:1]&[1:18:1] 117670k2 [1,1,1,-1511,-26667] 1 [398:1047:8]&[81:584:1]
117670l (1 curve)	1	2- 5+ 7+ 41-	2-  1 5+ 7+  2 -3  6  4
Curve Equation t Generators 117670l1 [1,0,0,-14601201,21485480681] 1 [1366:63267:1]
117670m (4 curves)	1	2- 5+ 7- 41+	2-  0 5+ 7- -4  6 -2  0
Curve Equation t Generators 117670m1 [1,-1,1,3887,-149583] 2 [1953:85358:1] 117670m2 [1,-1,1,-29733,-1588519] 4 [1511994424:13782827363:6229504] 117670m3 [1,-1,1,-147403,20392237] 2 [58974014147084994:-2598339361521075161:29970103730328] 117670m4 [1,-1,1,-449983,-116064619] 2 [61844:1167599:64]
117670n (1 curve)	1	2- 5+ 7- 41+	2- -1 5+ 7- -2  3 -6 -4
Curve Equation t Generators 117670n1 [1,1,1,-8686,308139] 1 [39:155:1]
117670o (2 curves)	0	2- 5+ 7- 41-	2-  1 5+ 7-  6 -1  0 -4
Curve Equation t 117670o1 [1,0,0,216814,12109316] 3 117670o2 [1,0,0,-2540026,-1794723620] 1
117670p (1 curve)	1	2- 5- 7+ 41+	2-  0 5- 7+ -1  1  7 -6
Curve Equation t Generators 117670p1 [1,-1,1,9360333,12260314691] 1 [-579:81814:1]
117670q (1 curve)	1	2- 5- 7- 41-	2-  0 5- 7-  1 -1 -7  6
Curve Equation t Generators 117670q1 [1,-1,1,5568,176531] 1 [31:599:1]

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