Cremona's table of elliptic curves

1638 = 2 · 3² · 7 · 13

Class	r	Atkin-Lehner	Eigenvalues
1638a (1 curve)	0	2+ 3+ 7+ 13-	2+ 3+  1 7+  5 13-  1 -1
Curve Equation t 1638a1 [1,-1,0,741,21797] 1
1638b (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  3 7-  1 13+  5 -1
Curve Equation t 1638b1 [1,-1,0,-33738,-2381068] 1
1638c (4 curves)	1	2+ 3+ 7- 13-	2+ 3+  0 7-  0 13- -6 -4
Curve Equation t Generators 1638c1 [1,-1,0,-957,11637] 6 [-9:144:1] 1638c2 [1,-1,0,-897,13113] 6 [-32:107:1] 1638c3 [1,-1,0,-1932,-14896] 2 [-35:112:1] 1638c4 [1,-1,0,6708,-116848] 2 [64:724:1]
1638d (2 curves)	1	2+ 3+ 7- 13-	2+ 3+ -3 7- -3 13-  3  5
Curve Equation t Generators 1638d1 [1,-1,0,-21,63] 3 [3:3:1] 1638d2 [1,-1,0,174,-964] 1 [19:85:1]
1638e (4 curves)	0	2+ 3- 7+ 13+	2+ 3- -2 7+ -4 13+  6  0
Curve Equation t 1638e1 [1,-1,0,7797,-181819] 2 1638e2 [1,-1,0,-38283,-1573435] 4 1638e3 [1,-1,0,-532203,-149255515] 2 1638e4 [1,-1,0,-281643,56492261] 2
1638f (1 curve)	0	2+ 3- 7+ 13+	2+ 3- -3 7+ -1 13+ -7  1
Curve Equation t 1638f1 [1,-1,0,-904356,333142096] 1
1638g (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  4 7+ -1 13+  0 -6
Curve Equation t 1638g1 [1,-1,0,30,98] 1
1638h (2 curves)	1	2+ 3- 7- 13+	2+ 3-  1 7- -5 13+  3 -1
Curve Equation t Generators 1638h1 [1,-1,0,6426,2238516] 1 [315:5796:1] 1638h2 [1,-1,0,-33070464,73207840986] 1 [3321:-1602:1]
1638i (4 curves)	1	2+ 3- 7- 13+	2+ 3- -2 7-  4 13+ -6 -4
Curve Equation t Generators 1638i1 [1,-1,0,-63,189] 2 [-6:21:1] 1638i2 [1,-1,0,-243,-1215] 4 [-9:18:1] 1638i3 [1,-1,0,-3753,-87561] 2 [-35:18:1] 1638i4 [1,-1,0,387,-6885] 2 [33:186:1]
1638j (3 curves)	0	2+ 3- 7- 13-	2+ 3-  0 7-  3 13-  0  2
Curve Equation t 1638j1 [1,-1,0,63,189] 1 1638j2 [1,-1,0,-1737,28485] 3 1638j3 [1,-1,0,-140967,20406843] 3
1638k (1 curve)	1	2- 3+ 7+ 13-	2- 3+ -1 7+ -5 13- -1 -1
Curve Equation t Generators 1638k1 [1,-1,1,82,-835] 1 [9:19:1]
1638l (1 curve)	1	2- 3+ 7- 13+	2- 3+ -3 7- -1 13+ -5 -1
Curve Equation t Generators 1638l1 [1,-1,1,-3749,89437] 1 [49:-172:1]
1638m (4 curves)	0	2- 3+ 7- 13-	2- 3+  0 7-  0 13-  6 -4
Curve Equation t 1638m1 [1,-1,1,-215,623] 6 1638m2 [1,-1,1,745,4079] 6 1638m3 [1,-1,1,-8615,-305585] 2 1638m4 [1,-1,1,-8075,-345977] 2
1638n (2 curves)	0	2- 3+ 7- 13-	2- 3+  3 7-  3 13- -3  5
Curve Equation t 1638n1 [1,-1,1,19,29] 3 1638n2 [1,-1,1,-191,-1511] 1
1638o (1 curve)	1	2- 3- 7+ 13+	2- 3- -1 7+ -3 13+ -5  1
Curve Equation t Generators 1638o1 [1,-1,1,-68,263] 1 [9:-23:1]
1638p (1 curve)	0	2- 3- 7+ 13-	2- 3-  1 7+  1 13-  1  7
Curve Equation t 1638p1 [1,-1,1,-977,12147] 1
1638q (4 curves)	0	2- 3- 7+ 13-	2- 3-  2 7+  4 13-  2 -4
Curve Equation t 1638q1 [1,-1,1,-509,4421] 4 1638q2 [1,-1,1,-1229,-10267] 4 1638q3 [1,-1,1,-17609,-894787] 2 1638q4 [1,-1,1,3631,-74419] 2
1638r (1 curve)	0	2- 3- 7+ 13-	2- 3- -4 7+  1 13- -4  2
Curve Equation t 1638r1 [1,-1,1,-41477,-3246595] 1
1638s (1 curve)	0	2- 3- 7- 13+	2- 3-  0 7-  5 13+  4  2
Curve Equation t 1638s1 [1,-1,1,-200,-23669] 1
1638t (3 curves)	1	2- 3- 7- 13-	2- 3- -3 7- -3 13-  3 -7
Curve Equation t Generators 1638t1 [1,-1,1,121,-4921] 1 [81:688:1] 1638t2 [1,-1,1,-1094,133589] 3 [-27:391:1] 1638t3 [1,-1,1,-234509,43769909] 3 [207:1912:1]

Data from Elliptic Curve Data by J. E. Cremona.
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Part of Computational Number Theory
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