Cremona's table of elliptic curves

6678 = 2 · 3² · 7 · 53

Class	r	Atkin-Lehner	Eigenvalues
6678a (2 curves)	1	2+ 3+ 7+ 53+	2+ 3+  2 7+  0 -2 -6  0
Curve Equation t Generators 6678a1 [1,-1,0,-1986,-35308] 2 [227:3229:1] 6678a2 [1,-1,0,-32226,-2218636] 2 [32695:318953:125]
6678b (2 curves)	0	2+ 3+ 7+ 53-	2+ 3+  2 7+  4  4  6  4
Curve Equation t 6678b1 [1,-1,0,-21,-31] 2 6678b2 [1,-1,0,9,-133] 2
6678c (1 curve)	0	2+ 3- 7+ 53+	2+ 3- -1 7+  1  0  7 -4
Curve Equation t 6678c1 [1,-1,0,24390,2447284] 1
6678d (1 curve)	1	2+ 3- 7+ 53-	2+ 3-  2 7+ -2  1 -3  1
Curve Equation t Generators 6678d1 [1,-1,0,-726,-317800] 1 [9580:28824:125]
6678e (2 curves)	1	2+ 3- 7+ 53-	2+ 3-  2 7+ -2 -6  4  8
Curve Equation t Generators 6678e1 [1,-1,0,39028779,-144211671563] 2 [110600385229526:-18789604598364523:4027268071] 6678e2 [1,-1,0,-291272661,-1532204382731] 2 [-601318450:-38492125159:79507]
6678f (1 curve)	1	2+ 3- 7- 53+	2+ 3-  3 7-  1 -4  3 -8
Curve Equation t Generators 6678f1 [1,-1,0,-6678,-216972] 1 [231:3129:1]
6678g (2 curves)	0	2+ 3- 7- 53-	2+ 3-  2 7-  0 -4 -2  0
Curve Equation t 6678g1 [1,-1,0,639,7465] 2 6678g2 [1,-1,0,-4131,77107] 2
6678h (1 curve)	0	2+ 3- 7- 53-	2+ 3-  2 7-  6  5  1 -3
Curve Equation t 6678h1 [1,-1,0,-126,-2156] 1
6678i (2 curves)	0	2- 3+ 7+ 53+	2- 3+ -2 7+ -4  4 -6  4
Curve Equation t 6678i1 [1,-1,1,-191,1027] 2 6678i2 [1,-1,1,79,3511] 2
6678j (2 curves)	1	2- 3+ 7+ 53-	2- 3+ -2 7+  0 -2  6  0
Curve Equation t Generators 6678j1 [1,-1,1,-221,1381] 2 [7:8:1] 6678j2 [1,-1,1,-3581,83365] 2 [-5:320:1]
6678k (2 curves)	1	2- 3- 7+ 53+	2- 3- -4 7+  4  2 -6  2
Curve Equation t Generators 6678k1 [1,-1,1,-572,-7185] 2 [47:237:1] 6678k2 [1,-1,1,-10112,-388785] 2 [153:1199:1]
6678l (1 curve)	0	2- 3- 7+ 53-	2- 3-  1 7+  1  2 -1 -2
Curve Equation t 6678l1 [1,-1,1,-335192,-74610597] 1
6678m (1 curve)	0	2- 3- 7+ 53-	2- 3-  1 7+ -3  4  3  0
Curve Equation t 6678m1 [1,-1,1,-47,-143] 1
6678n (4 curves)	0	2- 3- 7+ 53-	2- 3- -2 7+  0  2 -2  4
Curve Equation t 6678n1 [1,-1,1,-221,-1195] 2 6678n2 [1,-1,1,-401,1181] 4 6678n3 [1,-1,1,-5171,144281] 2 6678n4 [1,-1,1,1489,7985] 2
6678o (4 curves)	0	2- 3- 7+ 53-	2- 3- -2 7+  4  2  2  4
Curve Equation t 6678o1 [1,-1,1,-17096,864267] 4 6678o2 [1,-1,1,-19976,555531] 4 6678o3 [1,-1,1,-153536,-22737333] 2 6678o4 [1,-1,1,67504,4054731] 2
6678p (2 curves)	0	2- 3- 7- 53+	2- 3- -2 7- -4  0  6 -8
Curve Equation t 6678p1 [1,-1,1,-1166,-19875] 2 6678p2 [1,-1,1,-20246,-1103619] 2
6678q (2 curves)	0	2- 3- 7- 53+	2- 3- -2 7-  6  2 -4  0
Curve Equation t 6678q1 [1,-1,1,184,-1029] 2 6678q2 [1,-1,1,-1076,-9093] 2
6678r (2 curves)	0	2- 3- 7- 53+	2- 3-  4 7-  0 -4  2  6
Curve Equation t 6678r1 [1,-1,1,-266513,-55011711] 2 6678r2 [1,-1,1,-4311473,-3444688191] 2
6678s (1 curve)	1	2- 3- 7- 53-	2- 3-  0 7-  0  1 -1 -3
Curve Equation t Generators 6678s1 [1,-1,1,33010,20690461] 1 [-223:1595:1]
6678t (1 curve)	1	2- 3- 7- 53-	2- 3-  1 7- -3 -6  3 -2
Curve Equation t Generators 6678t1 [1,-1,1,733,1667] 1 [15:118:1]
6678u (1 curve)	1	2- 3- 7- 53-	2- 3- -3 7- -3  4 -1  0
Curve Equation t Generators 6678u1 [1,-1,1,6541,-326573] 1 [91:962:1]

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