Cremona's table of elliptic curves

27735 = 3 · 5 · 43²

Class	r	Atkin-Lehner	Eigenvalues
27735a (1 curve)	1	3+ 5+ 43+	1 3+ 5+  3 -5  0 -2  6
Curve Equation t Generators 27735a1 [1,1,0,-906048,-299787723] 1 [39867372:9301901509:729]
27735b (1 curve)	2	3+ 5+ 43-	0 3+ 5+  2 -5 -5  5  6
Curve Equation t Generators 27735b1 [0,-1,1,3355319,-11182531644] 1 [13588:1594687:1]&[48126:577799:27]
27735c (1 curve)	0	3+ 5+ 43-	2 3+ 5+  4 -3  5 -7  0
Curve Equation t 27735c1 [0,-1,1,17874,-3265009] 1
27735d (1 curve)	0	3+ 5- 43+	1 3+ 5-  1 -5  2  6 -6
Curve Equation t 27735d1 [1,1,0,-3847807,-2550869414] 1
27735e (2 curves)	0	3+ 5- 43+	-1 3+ 5-  4  4  2  8 -2
Curve Equation t 27735e1 [1,1,1,-1263830,-14662747150] 2 27735e2 [1,1,1,-97864835,-368956593088] 2
27735f (2 curves)	0	3- 5+ 43+	1 3- 5+ -4  4  2  8  2
Curve Equation t 27735f1 [1,0,1,-684,184357] 2 27735f2 [1,0,1,-52929,4635631] 2
27735g (8 curves)	1	3- 5+ 43-	1 3- 5+  0 -4 -2  2 -4
Curve Equation t Generators 27735g1 [1,0,1,-39,-14819] 2 [3526744849368307:-75364364872847791:8100013911787] 27735g2 [1,0,1,-9284,-340243] 4 [-120494409:-33080186:2352637] 27735g3 [1,0,1,-18529,447431] 4 [-5621:299039:343] 27735g4 [1,0,1,-147959,-21918073] 2 [436191545798750560:-18037639675092189729:247862504554496] 27735g5 [1,0,1,64676,3376247] 2 [2325144458:54653658487:6028568] 27735g6 [1,0,1,-249654,47966731] 4 [-37:7578:1] 27735g7 [1,0,1,-203429,66290321] 2 [4758:97463:8] 27735g8 [1,0,1,-3993879,3071802841] 2 [10798:89433:8]
27735h (1 curve)	1	3- 5+ 43-	-1 3- 5+ -1 -5  2  6  6
Curve Equation t Generators 27735h1 [1,0,0,-2081,31890] 1 [61:-395:1]
27735i (2 curves)	1	3- 5+ 43-	-1 3- 5+ -4 -2  2  0 -6
Curve Equation t Generators 27735i1 [1,0,0,-41641,-3208504] 2 [283:-2915:1] 27735i2 [1,0,0,4584,-9929619] 2 [2820:148359:1]
27735j (1 curve)	1	3- 5+ 43-	2 3- 5+ -4  1  5 -3  0
Curve Equation t Generators 27735j1 [0,1,1,-33282616,73893987601] 1 [24106:249611:8]
27735k (1 curve)	1	3- 5+ 43-	-2 3- 5+  0  5  1  5 -4
Curve Equation t Generators 27735k1 [0,1,1,-31026836,-67568222734] 1 [8872:596302:1]
27735l (4 curves)	0	3- 5- 43-	-1 3- 5-  0  4  6 -2  0
Curve Equation t 27735l1 [1,0,0,2735,-501568] 4 27735l2 [1,0,0,-80470,-8439325] 4 27735l3 [1,0,0,-219145,28420490] 2 27735l4 [1,0,0,-1273075,-552982768] 2
27735m (1 curve)	2	3- 5- 43-	-1 3- 5- -3 -5  0 -2 -6
Curve Equation t Generators 27735m1 [1,0,0,-490,3725] 1 [5:-40:1]&[-20:85:1]

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