Cremona's table of elliptic curves

6566 = 2 · 7² · 67

Class	r	Atkin-Lehner	Eigenvalues
6566a (2 curves)	0	2+ 7- 67+	2+  2 -4 7-  4 -4 -4  0
Curve Equation t 6566a1 [1,1,0,-312,-2260] 2 6566a2 [1,1,0,-5002,-138270] 2
6566b (2 curves)	0	2+ 7- 67+	2+ -2  4 7-  4  4  4  0
Curve Equation t 6566b1 [1,0,1,-15314,729264] 2 6566b2 [1,0,1,-245124,46691264] 2
6566c (2 curves)	1	2+ 7- 67-	2+  0  2 7-  0 -2  0 -2
Curve Equation t Generators 6566c1 [1,-1,0,-2501,-47531] 2 [1670:22481:8] 6566c2 [1,-1,0,-40021,-3071643] 2 [55842:393739:216]
6566d (2 curves)	1	2+ 7- 67-	2+  0 -2 7-  0  2  0  2
Curve Equation t Generators 6566d1 [1,-1,0,-122558,16548244] 2 [199:1:1] 6566d2 [1,-1,0,-1961038,1057495620] 2 [37:31366:1]
6566e (1 curve)	1	2+ 7- 67-	2+ -1  1 7-  2  7  2  2
Curve Equation t Generators 6566e1 [1,1,0,-172,428] 1 [-1:25:1]
6566f (2 curves)	1	2+ 7- 67-	2+  2 -2 7- -4 -2  2  8
Curve Equation t Generators 6566f1 [1,1,0,-17861,-4685491] 2 [3222849:50279305:9261] 6566f2 [1,1,0,-543141,-153759955] 2 [294531875967:-6220012803017:275894451]
6566g (1 curve)	1	2+ 7- 67-	2+  3 -1 7-  0  1 -6 -2
Curve Equation t Generators 6566g1 [1,-1,0,-3106315,2108021957] 1 [-44718:1427287:27]
6566h (1 curve)	1	2+ 7- 67-	2+ -3  1 7-  0 -1  6  2
Curve Equation t Generators 6566h1 [1,-1,0,-63394,-6127724] 1 [-145:76:1]
6566i (1 curve)	1	2- 7- 67+	2-  1  1 7- -4  3  0 -4
Curve Equation t Generators 6566i1 [1,0,0,-2745,38009] 1 [130:1307:1]
6566j (1 curve)	1	2- 7- 67+	2-  1 -1 7-  2  1 -4  0
Curve Equation t Generators 6566j1 [1,0,0,-106,-428] 1 [-6:4:1]
6566k (1 curve)	1	2- 7- 67+	2- -1  1 7-  2 -1  4  0
Curve Equation t Generators 6566k1 [1,1,1,-5195,141609] 1 [69:308:1]
6566l (2 curves)	1	2- 7- 67+	2-  2 -2 7- -4  2  4 -6
Curve Equation t Generators 6566l1 [1,1,1,356,-7043] 2 [85:761:1] 6566l2 [1,1,1,-4124,-93059] 2 [-43:105:1]
6566m (2 curves)	1	2- 7- 67+	2- -2  2 7- -4 -2 -4  6
Curve Equation t Generators 6566m1 [1,0,0,17443,2468017] 2 [-62:1103:1] 6566m2 [1,0,0,-202077,31312945] 2 [102:3379:1]
6566n (3 curves)	2	2- 7- 67-	2- -1 -3 7- -6 -5 -6 -2
Curve Equation t Generators 6566n1 [1,1,1,-8772,-261563] 1 [-71:133:1]&[-43:217:1] 6566n2 [1,1,1,-212612,37621317] 1 [-407:7749:1]&[-76139:2987305:343] 6566n3 [1,1,1,-17218552,27493481637] 1 [2393:-1001:1]&[6257:402787:1]
6566o (1 curve)	0	2- 7- 67-	2-  3  3 7- -4  5 -2  6
Curve Equation t 6566o1 [1,-1,1,-18801,-984287] 1
6566p (1 curve)	2	2- 7- 67-	2- -3 -3 7- -4 -5  2 -6
Curve Equation t Generators 6566p1 [1,-1,1,-384,2979] 1 [37:-215:1]&[-3:65:1]

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