Cremona's table of elliptic curves

83421 = 3² · 13 · 23 · 31

Class	r	Atkin-Lehner	Eigenvalues
83421a (2 curves)	1	3+ 13+ 23+ 31+	1 3+ -2 -2  4 13+  2 -6
Curve Equation t Generators 83421a1 [1,-1,0,-48,-45] 2 [10:15:1] 83421a2 [1,-1,0,-393,3060] 2 [16:18:1]
83421b (2 curves)	2	3+ 13+ 23- 31+	-1 3+  2 -2 -4 13+ -2 -6
Curve Equation t Generators 83421b1 [1,-1,1,-434,1648] 2 [-8:71:1]&[44:235:1] 83421b2 [1,-1,1,-3539,-79082] 2 [-34:49:1]&[-31:25:1]
83421c (1 curve)	1	3+ 13- 23+ 31-	0 3+ -1  0  0 13-  4 -6
Curve Equation t Generators 83421c1 [0,0,1,-3498,79630] 1 [34:-2:1]
83421d (1 curve)	0	3+ 13- 23- 31-	0 3+  1  0  0 13- -4 -6
Curve Equation t 83421d1 [0,0,1,-31482,-2150017] 1
83421e (2 curves)	0	3- 13+ 23+ 31+	1 3-  4  2 -4 13+ -8 -2
Curve Equation t 83421e1 [1,-1,0,-7920,359923] 2 83421e2 [1,-1,0,-137655,19690438] 2
83421f (1 curve)	0	3- 13+ 23+ 31+	-2 3-  1 -1  2 13+ -5  7
Curve Equation t 83421f1 [0,0,1,-158547,-24298736] 1
83421g (1 curve)	1	3- 13+ 23+ 31-	0 3-  1 -3  6 13+  5 -7
Curve Equation t Generators 83421g1 [0,0,1,-149322,-22209246] 1 [-830820770:-1133914:3723875]
83421h (2 curves)	0	3- 13+ 23- 31-	-1 3-  2  4 -2 13+ -4  0
Curve Equation t 83421h1 [1,-1,1,3091,-15564] 2 83421h2 [1,-1,1,-12704,-116652] 2
83421i (1 curve)	0	3- 13+ 23- 31-	2 3-  2 -2 -5 13+  2 -6
Curve Equation t 83421i1 [0,0,1,-17229,1579279] 1
83421j (1 curve)	1	3- 13- 23+ 31+	0 3-  0 -2 -1 13- -4  0
Curve Equation t Generators 83421j1 [0,0,1,-4471860,6446001550] 1 [32190214:9858938179:343]
83421k (1 curve)	1	3- 13- 23+ 31+	0 3- -1  3 -2 13- -3 -1
Curve Equation t Generators 83421k1 [0,0,1,-48,27] 1 [-7:4:1]
83421l (2 curves)	1	3- 13- 23+ 31+	1 3-  4 -4  6 13-  0  0
Curve Equation t Generators 83421l1 [1,-1,0,1935,-59832] 2 [13236:187017:64] 83421l2 [1,-1,0,-16200,-658287] 2 [1813220:20670949:8000]
83421m (1 curve)	1	3- 13- 23+ 31+	-1 3-  1 -1  5 13-  4  0
Curve Equation t Generators 83421m1 [1,-1,1,-3944417,3013190862] 1 [8158:52779:8]
83421n (2 curves)	1	3- 13- 23+ 31+	-1 3- -2  2  2 13- -2  6
Curve Equation t Generators 83421n1 [1,-1,1,-181346,24402696] 2 [2438004:13737600:6859] 83421n2 [1,-1,1,366169,142884942] 2 [864:32789:1]
83421o (2 curves)	1	3- 13- 23+ 31+	-1 3- -2  2 -4 13-  4  6
Curve Equation t Generators 83421o1 [1,-1,1,-14919251,-23107395630] 2 [643330:-24174279:125] 83421o2 [1,-1,1,-241479806,-1444276445034] 2 [-8980:5457:1]
83421p (1 curve)	1	3- 13- 23+ 31+	-2 3- -2  2 -3 13-  6 -6
Curve Equation t Generators 83421p1 [0,0,1,-2415351,-1444835790] 1 [1505170:163716548:125]
83421q (1 curve)	0	3- 13- 23+ 31-	2 3-  3 -3 -2 13-  3  5
Curve Equation t 83421q1 [0,0,1,-3981,86139] 1
83421r (1 curve)	0	3- 13- 23- 31+	0 3-  1  0 -1 13- -6  5
Curve Equation t 83421r1 [0,0,1,-282,21663] 1
83421s (2 curves)	0	3- 13- 23- 31+	1 3-  2  2  6 13-  6  6
Curve Equation t 83421s1 [1,-1,0,-1971,-33048] 2 83421s2 [1,-1,0,-936,-68445] 2
83421t (1 curve)	0	3- 13- 23- 31+	1 3-  3 -1 -5 13-  8  0
Curve Equation t 83421t1 [1,-1,0,-284845158,1850449960957] 1
83421u (2 curves)	1	3- 13- 23- 31-	-1 3-  0  0  2 13-  4 -4
Curve Equation t Generators 83421u1 [1,-1,1,-8600,605738] 2 [-36:949:1] 83421u2 [1,-1,1,-171815,27438284] 2 [-162:7222:1]
83421v (1 curve)	1	3- 13- 23- 31-	-1 3- -1  5 -1 13-  6  4
Curve Equation t Generators 83421v1 [1,-1,1,-1868,29828] 1 [9:112:1]
83421w (2 curves)	1	3- 13- 23- 31-	-1 3-  2  2  2 13-  6 -2
Curve Equation t Generators 83421w1 [1,-1,1,-1437269,2979772940] 2 [28458:4782478:1] 83421w2 [1,-1,1,-41098514,101117557568] 2 [-6384:324559:1]
83421x (1 curve)	1	3- 13- 23- 31-	-2 3-  1 -5 -6 13-  1  3
Curve Equation t Generators 83421x1 [0,0,1,-1407,16654] 1 [-2:-140:1]

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