Cremona's table of elliptic curves

56355 = 3 · 5 · 13 · 17²

Class	r	Atkin-Lehner	Eigenvalues
56355a (2 curves)	1	3+ 5+ 13+ 17+	-1 3+ 5+  2  0 13+ 17+  2
Curve Equation t Generators 56355a1 [1,1,1,-5786,-156346] 2 [-42:142:1] 56355a2 [1,1,1,7219,-744172] 2 [86:679:1]
56355b (8 curves)	2	3+ 5+ 13- 17+	-1 3+ 5+  0 -4 13- 17+ -4
Curve Equation t Generators 56355b1 [1,1,1,-31796,2168948] 2 [-186:1393:1]&[-858:17129:8] 56355b2 [1,1,1,-33241,1959134] 4 [-187:1389:1]&[-152:1954:1] 56355b3 [1,1,1,60684,11126214] 2 [-67:2634:1]&[35878:2388849:8] 56355b4 [1,1,1,-150286,-20607142] 4 [2432:-119562:1]&[-233:1468:1] 56355b5 [1,1,1,174839,-97206592] 2 [366:3814:1]&[392:5439:1] 56355b6 [1,1,1,-2348131,-1385908456] 4 [-7066:3941:8]&[15886:330183:8] 56355b7 [1,1,1,-2291776,-1455518152] 2 [353606:-74475651:8]&[26717474:2588983641:2744] 56355b8 [1,1,1,-37570006,-88651625956] 2 [-30939468982:15466000059:8741816]&[275886:-50499817:8]
56355c (2 curves)	0	3+ 5+ 13- 17+	-1 3+ 5+  2  4 13- 17+ -8
Curve Equation t 56355c1 [1,1,1,-24527436,42714935508] 2 56355c2 [1,1,1,29196219,203950368894] 2
56355d (1 curve)	0	3+ 5+ 13- 17+	2 3+ 5+  3  5 13- 17+  2
Curve Equation t 56355d1 [0,-1,1,-96,-3289] 1
56355e (1 curve)	0	3+ 5+ 13- 17+	2 3+ 5+ -4  4 13- 17+ -2
Curve Equation t 56355e1 [0,-1,1,-13696,-612399] 1
56355f (1 curve)	1	3+ 5+ 13- 17-	-1 3+ 5+ -4  5 13- 17-  5
Curve Equation t Generators 56355f1 [1,1,1,-200861,-98333692] 1 [5052:355048:1]
56355g (2 curves)	2	3+ 5- 13+ 17+	-1 3+ 5-  0  0 13+ 17+ -6
Curve Equation t Generators 56355g1 [1,1,1,-14405,659450] 2 [1866:-1024:27]&[-506:9449:8] 56355g2 [1,1,1,-14660,634562] 2 [-1082:3797:8]&[-58:1166:1]
56355h (1 curve)	2	3+ 5- 13+ 17+	-1 3+ 5- -4 -1 13+ 17+  3
Curve Equation t Generators 56355h1 [1,1,1,-40,122] 1 [-8:6:1]&[2:-9:1]
56355i (1 curve)	0	3+ 5- 13+ 17+	2 3+ 5-  1 -5 13+ 17+ -6
Curve Equation t 56355i1 [0,-1,1,-19170,-1598569] 1
56355j (2 curves)	1	3+ 5- 13- 17+	0 3+ 5-  4  3 13- 17+ -1
Curve Equation t Generators 56355j1 [0,-1,1,-1235,17111] 1 [-13:175:1] 56355j2 [0,-1,1,-4295,-88612] 1 [-46:97:1]
56355k (2 curves)	1	3+ 5- 13- 17+	-1 3+ 5-  2 -2 13- 17+  4
Curve Equation t Generators 56355k1 [1,1,1,-37355,37352] 2 [-168:1351:1] 56355k2 [1,1,1,149390,485540] 2 [53:2898:1]
56355l (4 curves)	1	3+ 5- 13- 17+	-1 3+ 5- -4  0 13- 17+  4
Curve Equation t Generators 56355l1 [1,1,1,-39310,1685162] 4 [-118:2226:1] 56355l2 [1,1,1,-283515,-57021720] 4 [-2610:8815:8] 56355l3 [1,1,1,35830,-177861868] 2 [885:-23852:1] 56355l4 [1,1,1,-4510140,-3688537920] 2 [-9810:5215:8]
56355m (1 curve)	1	3+ 5- 13- 17+	2 3+ 5-  2 -3 13- 17+  7
Curve Equation t Generators 56355m1 [0,-1,1,-14580,664301] 1 [-138510:84793:1000]
56355n (2 curves)	0	3- 5+ 13+ 17+	-1 3- 5+  0  0 13+ 17+ -6
Curve Equation t 56355n1 [1,0,0,-4163051,3269020080] 2 56355n2 [1,0,0,-4236746,3147261201] 2
56355o (1 curve)	0	3- 5+ 13+ 17+	2 3- 5+ -3  1 13+ 17+ -2
Curve Equation t 56355o1 [0,1,1,-55006,5080585] 1
56355p (1 curve)	1	3- 5+ 13+ 17-	-1 3- 5+  4  1 13+ 17-  3
Curve Equation t Generators 56355p1 [1,0,0,-11566,681221] 1 [-35:1039:1]
56355q (1 curve)	1	3- 5+ 13- 17+	0 3- 5+ -2 -2 13- 17+  2
Curve Equation t Generators 56355q1 [0,1,1,-1541,-27490] 1 [1470:6200:27]
56355r (2 curves)	1	3- 5+ 13- 17+	-1 3- 5+ -2  2 13- 17+  4
Curve Equation t Generators 56355r1 [1,0,0,-10795601,259080456] 2 [6316:425842:1] 56355r2 [1,0,0,43173704,2083242965] 2 [48986234:5788944383:10648]
56355s (2 curves)	0	3- 5+ 13- 17-	0 3- 5+ -4 -3 13- 17- -1
Curve Equation t 56355s1 [0,1,1,-357011,81925685] 3 56355s2 [0,1,1,-1241351,-442797454] 1
56355t (1 curve)	0	3- 5+ 13- 17-	2 3- 5+ -2  3 13- 17-  7
Curve Equation t 56355t1 [0,1,1,-4213716,3238429925] 1
56355u (1 curve)	1	3- 5- 13+ 17+	0 3- 5- -2 -2 13+ 17+  2
Curve Equation t Generators 56355u1 [0,1,1,-188235,50659931] 1 [555:-10838:1]
56355v (4 curves)	0	3- 5- 13- 17+	1 3- 5- -4  4 13- 17+  0
Curve Equation t 56355v1 [1,0,1,65586087,323056478863] 2 56355v2 [1,0,1,-498867038,3460964291363] 4 56355v3 [1,0,1,-2483032663,-44537589509887] 2 56355v4 [1,0,1,-7545951413,252287875905113] 2
56355w (2 curves)	2	3- 5- 13- 17+	-1 3- 5- -2 -4 13- 17+ -8
Curve Equation t Generators 56355w1 [1,0,0,-84870,8689275] 2 [75:-1695:1]&[-315:2205:1] 56355w2 [1,0,0,101025,41518332] 2 [3339:-195597:1]&[-231:2538:1]
56355x (4 curves)	0	3- 5- 13- 17+	-1 3- 5-  4  4 13- 17+ -4
Curve Equation t 56355x1 [1,0,0,-7520,240207] 4 56355x2 [1,0,0,-20525,-818400] 4 56355x3 [1,0,0,53170,-5343273] 2 56355x4 [1,0,0,-302300,-63992355] 2
56355y (1 curve)	0	3- 5- 13- 17+	-1 3- 5-  4 -5 13- 17+  5
Curve Equation t 56355y1 [1,0,0,-58048835,-482707086078] 1
56355z (1 curve)	0	3- 5- 13- 17+	2 3- 5-  4 -4 13- 17+ -2
Curve Equation t 56355z1 [0,1,1,-3958240,-3032464319] 1

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