Cremona's table of elliptic curves

12864 = 2⁶ · 3 · 67

Class	r	Atkin-Lehner	Eigenvalues
12864a (1 curve)	1	2+ 3+ 67+	2+ 3+  1 -5  4  4  6  2
Curve Equation t Generators 12864a1 [0,-1,0,-65,1089] 1 [1:32:1]
12864b (1 curve)	1	2+ 3+ 67+	2+ 3+  2  2  0  4 -7 -7
Curve Equation t Generators 12864b1 [0,-1,0,-7,-83] 1 [74:189:8]
12864c (3 curves)	1	2+ 3+ 67+	2+ 3+  3 -1  0  4 -6 -2
Curve Equation t Generators 12864c1 [0,-1,0,-9249,363681] 1 [25:384:1] 12864c2 [0,-1,0,51231,496737] 1 [7369:632832:1] 12864c3 [0,-1,0,-656289,-223967199] 1 [5586365715575:477131918278656:756058031]
12864d (1 curve)	0	2+ 3+ 67-	2+ 3+  1 -3  2  2 -4  4
Curve Equation t 12864d1 [0,-1,0,335,-47] 1
12864e (1 curve)	0	2+ 3+ 67-	2+ 3+  1  5  2  2  0  4
Curve Equation t 12864e1 [0,-1,0,40,-366] 1
12864f (2 curves)	0	2+ 3+ 67-	2+ 3+  2 -2  4 -4  6  4
Curve Equation t 12864f1 [0,-1,0,-257,1665] 2 12864f2 [0,-1,0,-97,3553] 2
12864g (4 curves)	0	2+ 3+ 67-	2+ 3+ -2  0 -4  2  2  4
Curve Equation t 12864g1 [0,-1,0,-609,-1311] 2 12864g2 [0,-1,0,-5729,167649] 4 12864g3 [0,-1,0,-91489,10681825] 2 12864g4 [0,-1,0,-1889,384993] 2
12864h (1 curve)	2	2+ 3+ 67-	2+ 3+ -2  2 -4 -4 -3 -5
Curve Equation t Generators 12864h1 [0,-1,0,1,633] 1 [8:33:1]&[16:67:1]
12864i (2 curves)	0	2+ 3+ 67-	2+ 3+ -2  2 -4 -4  6  4
Curve Equation t 12864i1 [0,-1,0,-97447209,-370223618391] 2 12864i2 [0,-1,0,-97447169,-370223937567] 2
12864j (1 curve)	0	2+ 3+ 67-	2+ 3+  3 -3  6  6 -4  4
Curve Equation t 12864j1 [0,-1,0,-64,226] 1
12864k (1 curve)	0	2+ 3- 67+	2+ 3-  0  0  2  4 -3 -5
Curve Equation t 12864k1 [0,1,0,-5493,-159021] 1
12864l (1 curve)	0	2+ 3- 67+	2+ 3-  1 -5 -2  2  0 -4
Curve Equation t 12864l1 [0,1,0,40,366] 1
12864m (1 curve)	0	2+ 3- 67+	2+ 3- -2 -2  4 -4 -3  5
Curve Equation t 12864m1 [0,1,0,1,-633] 1
12864n (2 curves)	0	2+ 3- 67+	2+ 3- -2 -2  4 -4  6 -4
Curve Equation t 12864n1 [0,1,0,-97447209,370223618391] 2 12864n2 [0,1,0,-97447169,370223937567] 2
12864o (1 curve)	0	2+ 3- 67+	2+ 3-  3  3  2 -2  0  4
Curve Equation t 12864o1 [0,1,0,-49,143] 1
12864p (1 curve)	0	2+ 3- 67+	2+ 3-  3  3 -6  6 -4 -4
Curve Equation t 12864p1 [0,1,0,-64,-226] 1
12864q (1 curve)	0	2+ 3- 67+	2+ 3-  4 -4  6  4 -3  7
Curve Equation t 12864q1 [0,1,0,-101,387] 1
12864r (1 curve)	1	2+ 3- 67-	2+ 3-  0  0  6 -4 -7  5
Curve Equation t Generators 12864r1 [0,1,0,7,9] 1 [0:3:1]
12864s (1 curve)	1	2+ 3- 67-	2+ 3- -1 -3  0  4  2  2
Curve Equation t Generators 12864s1 [0,1,0,-161,-5697] 1 [561:512:27]
12864t (1 curve)	1	2+ 3- 67-	2+ 3-  2 -2  0  4 -7  7
Curve Equation t Generators 12864t1 [0,1,0,-7,83] 1 [2:9:1]
12864u (2 curves)	1	2+ 3- 67-	2+ 3- -2  2  4  0  6 -4
Curve Equation t Generators 12864u1 [0,1,0,-2369,43551] 2 [25:24:1] 12864u2 [0,1,0,-1729,68255] 2 [-37:288:1]
12864v (1 curve)	1	2+ 3- 67-	2+ 3-  3 -3  0 -4  2  2
Curve Equation t Generators 12864v1 [0,1,0,-50849,4396479] 1 [115:288:1]
12864w (2 curves)	1	2+ 3- 67-	2+ 3- -4  0  0 -2  2 -4
Curve Equation t Generators 12864w1 [0,1,0,235,-741] 2 [7:36:1] 12864w2 [0,1,0,-1105,-7441] 2 [-25:72:1]
12864x (2 curves)	0	2- 3+ 67+	2- 3+  0  0  0 -6 -6  4
Curve Equation t 12864x1 [0,-1,0,-88,-290] 2 12864x2 [0,-1,0,-73,-407] 2
12864y (1 curve)	2	2- 3+ 67+	2- 3+  0  0 -6 -4 -7 -5
Curve Equation t Generators 12864y1 [0,-1,0,7,-9] 1 [2:3:1]&[10:31:1]
12864z (1 curve)	0	2- 3+ 67+	2- 3+ -1 -1  0  4  6  6
Curve Equation t 12864z1 [0,-1,0,4,-6] 1
12864ba (1 curve)	0	2- 3+ 67+	2- 3+ -1  3  0  4  2 -2
Curve Equation t 12864ba1 [0,-1,0,-161,5697] 1
12864bb (2 curves)	0	2- 3+ 67+	2- 3+ -2 -2 -4  0  6  4
Curve Equation t 12864bb1 [0,-1,0,-2369,-43551] 2 12864bb2 [0,-1,0,-1729,-68255] 2
12864bc (1 curve)	0	2- 3+ 67+	2- 3+  3  3  0 -4  2 -2
Curve Equation t 12864bc1 [0,-1,0,-50849,-4396479] 1
12864bd (2 curves)	0	2- 3+ 67+	2- 3+ -4  0  0 -2  2  4
Curve Equation t 12864bd1 [0,-1,0,235,741] 2 12864bd2 [0,-1,0,-1105,7441] 2
12864be (1 curve)	1	2- 3+ 67-	2- 3+  0  0 -2  4 -3  5
Curve Equation t Generators 12864be1 [0,-1,0,-5493,159021] 1 [330:243:8]
12864bf (1 curve)	1	2- 3+ 67-	2- 3+  3 -3 -2 -2  0 -4
Curve Equation t Generators 12864bf1 [0,-1,0,-49,-143] 1 [9:8:1]
12864bg (1 curve)	1	2- 3+ 67-	2- 3+  4  4 -6  4 -3 -7
Curve Equation t Generators 12864bg1 [0,-1,0,-101,-387] 1 [106:165:8]
12864bh (1 curve)	1	2- 3- 67+	2- 3-  1  3 -2  2 -4 -4
Curve Equation t Generators 12864bh1 [0,1,0,335,47] 1 [11:72:1]
12864bi (2 curves)	1	2- 3- 67+	2- 3-  2  2 -4 -4  6 -4
Curve Equation t Generators 12864bi1 [0,1,0,-257,-1665] 2 [5355:32544:125] 12864bi2 [0,1,0,-97,-3553] 2 [167:2160:1]
12864bj (4 curves)	1	2- 3- 67+	2- 3- -2  0  4  2  2 -4
Curve Equation t Generators 12864bj1 [0,1,0,-609,1311] 2 [-105:1628:27] 12864bj2 [0,1,0,-5729,-167649] 4 [-1508331:902060:35937] 12864bj3 [0,1,0,-91489,-10681825] 2 [2999:163392:1] 12864bj4 [0,1,0,-1889,-384993] 2 [327291927699:-8941245115060:437245479]
12864bk (2 curves)	0	2- 3- 67-	2- 3-  0  0  0 -6 -6 -4
Curve Equation t 12864bk1 [0,1,0,-88,290] 2 12864bk2 [0,1,0,-73,407] 2
12864bl (1 curve)	0	2- 3- 67-	2- 3-  1  5 -4  4  6 -2
Curve Equation t 12864bl1 [0,1,0,-65,-1089] 1
12864bm (1 curve)	0	2- 3- 67-	2- 3- -1  1  0  4  6 -6
Curve Equation t 12864bm1 [0,1,0,4,6] 1
12864bn (3 curves)	0	2- 3- 67-	2- 3-  3  1  0  4 -6  2
Curve Equation t 12864bn1 [0,1,0,-9249,-363681] 1 12864bn2 [0,1,0,51231,-496737] 1 12864bn3 [0,1,0,-656289,223967199] 1

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