Cremona's table of elliptic curves

5550 = 2 · 3 · 5² · 37

Class	r	Atkin-Lehner	Eigenvalues
5550a (2 curves)	1	2+ 3+ 5+ 37+	2+ 3+ 5+  1  3  1  3 -7
Curve Equation t Generators 5550a1 [1,1,0,50,-500] 1 [15:55:1] 5550a2 [1,1,0,-3700,-88250] 1 [345:6140:1]
5550b (2 curves)	1	2+ 3+ 5+ 37+	2+ 3+ 5+  1  3 -2 -3  2
Curve Equation t Generators 5550b1 [1,1,0,-2084900,-1546878000] 1 [959795:939822440:1] 5550b2 [1,1,0,-184100900,-961538430000] 1 [9237606005693783525:9044659416548768586200:9624179685511]
5550c (1 curve)	1	2+ 3+ 5+ 37+	2+ 3+ 5+  2 -2  1 -1 -4
Curve Equation t Generators 5550c1 [1,1,0,-260,-1680] 1 [-11:6:1]
5550d (2 curves)	1	2+ 3+ 5+ 37+	2+ 3+ 5+ -4 -2 -2  2  2
Curve Equation t Generators 5550d1 [1,1,0,-25,625] 2 [0:25:1] 5550d2 [1,1,0,-1275,16875] 2 [15:30:1]
5550e (1 curve)	0	2+ 3+ 5+ 37-	2+ 3+ 5+  5 -5  1  5 -3
Curve Equation t 5550e1 [1,1,0,-7025,295125] 1
5550f (1 curve)	0	2+ 3+ 5- 37+	2+ 3+ 5-  0  6 -5 -7 -2
Curve Equation t 5550f1 [1,1,0,-47700,-4029750] 1
5550g (2 curves)	0	2+ 3+ 5- 37+	2+ 3+ 5-  2 -2  6 -6 -4
Curve Equation t 5550g1 [1,1,0,-54185,4961925] 2 5550g2 [1,1,0,-873385,313800325] 2
5550h (1 curve)	2	2+ 3+ 5- 37+	2+ 3+ 5- -4 -2 -4 -2 -7
Curve Equation t Generators 5550h1 [1,1,0,-75,225] 1 [20:-95:1]&[-9:21:1]
5550i (1 curve)	0	2+ 3+ 5- 37+	2+ 3+ 5-  5  1  0  3  8
Curve Equation t 5550i1 [1,1,0,-4575,757125] 1
5550j (1 curve)	1	2+ 3+ 5- 37-	2+ 3+ 5-  0 -2  1  5 -2
Curve Equation t Generators 5550j1 [1,1,0,-6450,-103500] 1 [-31:276:1]
5550k (1 curve)	1	2+ 3+ 5- 37-	2+ 3+ 5- -1  5  0 -1  0
Curve Equation t Generators 5550k1 [1,1,0,-5830,-173900] 1 [115:775:1]
5550l (2 curves)	1	2+ 3+ 5- 37-	2+ 3+ 5- -2  0 -2 -2 -2
Curve Equation t Generators 5550l1 [1,1,0,-315,2025] 2 [0:45:1] 5550l2 [1,1,0,-365,1275] 2 [-1:41:1]
5550m (6 curves)	0	2+ 3- 5+ 37+	2+ 3- 5+  0  4  2 -2  4
Curve Equation t 5550m1 [1,0,1,-21126,4066648] 2 5550m2 [1,0,1,-533126,149474648] 4 5550m3 [1,0,1,-733126,27074648] 4 5550m4 [1,0,1,-8525126,9580034648] 2 5550m5 [1,0,1,-7578126,-7995265352] 2 5550m6 [1,0,1,2911874,216614648] 2
5550n (1 curve)	0	2+ 3- 5+ 37+	2+ 3- 5+ -3  1 -1  1 -5
Curve Equation t 5550n1 [1,0,1,-21626,-1225852] 1
5550o (2 curves)	1	2+ 3- 5+ 37-	2+ 3- 5+  0 -2  2 -6  6
Curve Equation t Generators 5550o1 [1,0,1,-28651,-2949802] 2 [367:5816:1] 5550o2 [1,0,1,-528651,-147949802] 2 [-418:396:1]
5550p (1 curve)	1	2+ 3- 5+ 37-	2+ 3- 5+  3 -5  2 -3 -6
Curve Equation t Generators 5550p1 [1,0,1,-3251,72398] 1 [12:181:1]
5550q (1 curve)	1	2+ 3- 5+ 37-	2+ 3- 5+ -3  1 -1  3  3
Curve Equation t Generators 5550q1 [1,0,1,424,21548] 1 [42:316:1]
5550r (1 curve)	1	2+ 3- 5- 37+	2+ 3- 5- -2 -2  5 -5  0
Curve Equation t Generators 5550r1 [1,0,1,-326,2048] 1 [2:36:1]
5550s (1 curve)	1	2+ 3- 5- 37+	2+ 3- 5-  4 -2 -4 -2 -3
Curve Equation t Generators 5550s1 [1,0,1,78674,-21105952] 1 [1477:56861:1]
5550t (2 curves)	0	2+ 3- 5- 37-	2+ 3- 5-  2  6 -1  3  8
Curve Equation t 5550t1 [1,0,1,-1201,-1852] 3 5550t2 [1,0,1,-70576,-7222402] 1
5550u (2 curves)	0	2+ 3- 5- 37-	2+ 3- 5- -2  4  6  6  2
Curve Equation t 5550u1 [1,0,1,-1201,12548] 2 5550u2 [1,0,1,-6201,-177452] 2
5550v (2 curves)	0	2- 3+ 5+ 37+	2- 3+ 5+  1  3  7  3 -1
Curve Equation t 5550v1 [1,1,1,3162,-185469] 1 5550v2 [1,1,1,-177213,-28823469] 1
5550w (2 curves)	0	2- 3+ 5+ 37+	2- 3+ 5+ -2  6  1 -3  8
Curve Equation t 5550w1 [1,1,1,-30013,-231469] 1 5550w2 [1,1,1,-1764388,-902800219] 1
5550x (4 curves)	0	2- 3+ 5+ 37+	2- 3+ 5+  4  6 -2  6  2
Curve Equation t 5550x1 [1,1,1,-7813,323531] 2 5550x2 [1,1,1,-132813,18573531] 2 5550x3 [1,1,1,57812,-2695219] 2 5550x4 [1,1,1,-262188,-23175219] 2
5550y (1 curve)	1	2- 3+ 5+ 37-	2- 3+ 5+  1 -1  3 -3 -5
Curve Equation t Generators 5550y1 [1,1,1,37,-5719] 1 [35:182:1]
5550z (1 curve)	1	2- 3+ 5+ 37-	2- 3+ 5+ -1 -5 -2 -1  6
Curve Equation t Generators 5550z1 [1,1,1,-4588,7600781] 1 [-25:2787:1]
5550ba (1 curve)	1	2- 3+ 5+ 37-	2- 3+ 5+  2 -2 -5  5  0
Curve Equation t Generators 5550ba1 [1,1,1,-13,11] 1 [1:0:1]
5550bb (1 curve)	1	2- 3+ 5+ 37-	2- 3+ 5+ -4 -2  4  2 -3
Curve Equation t Generators 5550bb1 [1,1,1,3147,-167589] 1 [151:1868:1]
5550bc (4 curves)	1	2- 3+ 5+ 37-	2- 3+ 5+ -4  4 -2  2  0
Curve Equation t Generators 5550bc1 [1,1,1,-4878463,4145335781] 4 [65:61842:1] 5550bc2 [1,1,1,-4886463,4131047781] 4 [871:22730:1] 5550bc3 [1,1,1,-8011463,-1800202219] 2 [5105:298072:1] 5550bc4 [1,1,1,-1889463,9148025781] 2 [2721:154080:1]
5550bd (2 curves)	1	2- 3+ 5- 37+	2- 3+ 5-  2  4 -6 -6  2
Curve Equation t Generators 5550bd1 [1,1,1,-48,81] 2 [-5:17:1] 5550bd2 [1,1,1,-248,-1519] 2 [-9:13:1]
5550be (1 curve)	1	2- 3- 5+ 37+	2- 3- 5+  0 -2 -1 -5 -2
Curve Equation t Generators 5550be1 [1,0,0,-258,-828] 1 [-12:30:1]
5550bf (4 curves)	1	2- 3- 5+ 37+	2- 3- 5+  0 -4 -6 -6  8
Curve Equation t Generators 5550bf1 [1,0,0,387,-783] 2 [12:69:1] 5550bf2 [1,0,0,-1613,-6783] 4 [-32:127:1] 5550bf3 [1,0,0,-20113,-1098283] 2 [-82:77:1] 5550bf4 [1,0,0,-15113,708717] 2 [82:109:1]
5550bg (1 curve)	1	2- 3- 5+ 37+	2- 3- 5+ -3  5 -3 -3 -7
Curve Equation t Generators 5550bg1 [1,0,0,-4557938,3745071492] 1 [1252:-1826:1]
5550bh (1 curve)	1	2- 3- 5+ 37+	2- 3- 5+ -3 -5  2  7 -2
Curve Equation t Generators 5550bh1 [1,0,0,5062,-71508] 1 [142:1804:1]
5550bi (1 curve)	0	2- 3- 5+ 37-	2- 3- 5+  0  6  5  7 -2
Curve Equation t 5550bi1 [1,0,0,-1908,-32238] 1
5550bj (1 curve)	0	2- 3- 5+ 37-	2- 3- 5+ -1 -1 -2  7 -2
Curve Equation t 5550bj1 [1,0,0,37,-333] 1
5550bk (1 curve)	0	2- 3- 5+ 37-	2- 3- 5+ -3 -3  5 -5  1
Curve Equation t 5550bk1 [1,0,0,-88,542] 1
5550bl (1 curve)	0	2- 3- 5+ 37-	2- 3- 5+  4 -2  4  2 -7
Curve Equation t 5550bl1 [1,0,0,-1888,31892] 1
5550bm (4 curves)	0	2- 3- 5+ 37-	2- 3- 5+  4  4 -2  2  8
Curve Equation t 5550bm1 [1,0,0,-35584713,-76835396583] 4 5550bm2 [1,0,0,-559872713,-5098990148583] 4 5550bm3 [1,0,0,-8957952713,-326333948228583] 2 5550bm4 [1,0,0,-550400713,-5279839044583] 2
5550bn (1 curve)	0	2- 3- 5- 37+	2- 3- 5-  1  5  0  1  0
Curve Equation t 5550bn1 [1,0,0,-145763,-21445983] 1
5550bo (2 curves)	0	2- 3- 5- 37+	2- 3- 5-  2  0  2  2 -2
Curve Equation t 5550bo1 [1,0,0,-7888,268892] 2 5550bo2 [1,0,0,-9138,177642] 2
5550bp (1 curve)	1	2- 3- 5- 37-	2- 3- 5- -2 -2 -1  1 -4
Curve Equation t Generators 5550bp1 [1,0,0,-6513,-196983] 1 [-48:99:1]
5550bq (2 curves)	1	2- 3- 5- 37-	2- 3- 5- -2 -2 -6  6 -4
Curve Equation t Generators 5550bq1 [1,0,0,-1354638,622949892] 2 [956:13730:1] 5550bq2 [1,0,0,-21834638,39268709892] 2 [3852:109074:1]
5550br (1 curve)	1	2- 3- 5- 37-	2- 3- 5- -5  1  0 -3  8
Curve Equation t Generators 5550br1 [1,0,0,-183,6057] 1 [42:-291:1]

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