Cremona's table of elliptic curves

12992 = 2⁶ · 7 · 29

Class	r	Atkin-Lehner	Eigenvalues
12992a (2 curves)	1	2+ 7+ 29+	2+  0  2 7+  6 -2 -4  8
Curve Equation t Generators 12992a1 [0,0,0,-19,-12] 2 [-156:285:64] 12992a2 [0,0,0,-164,800] 2 [-8:40:1]
12992b (1 curve)	1	2+ 7+ 29+	2+  1  3 7+  1  1 -4  4
Curve Equation t Generators 12992b1 [0,1,0,-6529,201439] 1 [45:28:1]
12992c (1 curve)	1	2+ 7+ 29+	2+ -1 -1 7+  3 -3  0 -4
Curve Equation t Generators 12992c1 [0,-1,0,924,-5978] 1 [7:28:1]
12992d (1 curve)	1	2+ 7+ 29+	2+ -1  2 7+  0  0  6 -7
Curve Equation t Generators 12992d1 [0,-1,0,-7,-7] 1 [16:61:1]
12992e (1 curve)	1	2+ 7+ 29+	2+ -3  3 7+ -3  1 -8 -4
Curve Equation t Generators 12992e1 [0,0,0,-31,-68] 1 [8:14:1]
12992f (2 curves)	0	2+ 7+ 29-	2+  0  0 7+  4  0 -4 -4
Curve Equation t 12992f1 [0,0,0,-19340,1118448] 2 12992f2 [0,0,0,-316300,68468976] 2
12992g (1 curve)	0	2+ 7+ 29-	2+ -1  0 7+  6 -4  6  5
Curve Equation t 12992g1 [0,-1,0,27,61] 1
12992h (2 curves)	2	2+ 7+ 29-	2+ -2 -2 7+  0 -6  4 -2
Curve Equation t Generators 12992h1 [0,1,0,-29,-29] 2 [-5:4:1]&[-2:5:1] 12992h2 [0,1,0,111,-113] 2 [2:11:1]&[3:16:1]
12992i (1 curve)	0	2+ 7+ 29-	2+ -3  0 7+ -2  0  2 -1
Curve Equation t 12992i1 [0,0,0,-160,-992] 1
12992j (4 curves)	0	2+ 7- 29+	2+  0  2 7-  4  2  6  0
Curve Equation t 12992j1 [0,0,0,-104,40] 2 12992j2 [0,0,0,-1084,-13680] 4 12992j3 [0,0,0,-17324,-877648] 2 12992j4 [0,0,0,-524,-27792] 2
12992k (2 curves)	0	2+ 7- 29+	2+  0  2 7- -6 -2 -4 -8
Curve Equation t 12992k1 [0,0,0,-19,12] 2 12992k2 [0,0,0,-164,-800] 2
12992l (1 curve)	0	2+ 7- 29+	2+  1 -1 7- -3 -3  0  4
Curve Equation t 12992l1 [0,1,0,924,5978] 1
12992m (1 curve)	0	2+ 7- 29+	2+  1 -1 7-  5  5 -4  4
Curve Equation t 12992m1 [0,1,0,-1,-929] 1
12992n (1 curve)	0	2+ 7- 29+	2+  1  2 7-  0  0  6  7
Curve Equation t 12992n1 [0,1,0,-7,7] 1
12992o (2 curves)	0	2+ 7- 29+	2+ -1  3 7-  3  1  0  4
Curve Equation t 12992o1 [0,-1,0,-929,108577] 1 12992o2 [0,-1,0,8351,-2899999] 1
12992p (1 curve)	0	2+ 7- 29+	2+  3  3 7-  3  1 -8  4
Curve Equation t 12992p1 [0,0,0,-31,68] 1
12992q (1 curve)	1	2+ 7- 29-	2+  1  1 7- -1 -1  2  4
Curve Equation t Generators 12992q1 [0,1,0,-145,1711] 1 [15:56:1]
12992r (2 curves)	1	2+ 7- 29-	2+  1  4 7- -2 -4 -2 -5
Curve Equation t Generators 12992r1 [0,1,0,79,17] 1 [8:35:1] 12992r2 [0,1,0,-8601,-309943] 1 [208:2635:1]
12992s (2 curves)	1	2+ 7- 29-	2+  2  2 7-  0 -2  0 -6
Curve Equation t Generators 12992s1 [0,-1,0,303,2513] 2 [11:84:1] 12992s2 [0,-1,0,-2017,27105] 2 [-48:105:1]
12992t (2 curves)	1	2+ 7- 29-	2+ -2  0 7-  0 -4  2 -6
Curve Equation t Generators 12992t1 [0,1,0,-8513,355231] 2 [-51:812:1] 12992t2 [0,1,0,-143073,20781439] 2 [210:203:1]
12992u (2 curves)	1	2+ 7- 29-	2+ -2 -2 7-  4  2  4 -2
Curve Equation t Generators 12992u1 [0,1,0,-609,5887] 2 [3:64:1] 12992u2 [0,1,0,-9889,375231] 2 [50:91:1]
12992v (2 curves)	1	2+ 7- 29-	2+ -2 -2 7- -4  2 -4 -2
Curve Equation t Generators 12992v1 [0,1,0,-135969,-30615233] 2 [509:5684:1] 12992v2 [0,1,0,-2511649,-1532520129] 2 [-910:581:1]
12992w (4 curves)	0	2- 7+ 29+	2-  0  2 7+ -4  2  6  0
Curve Equation t 12992w1 [0,0,0,-104,-40] 2 12992w2 [0,0,0,-1084,13680] 4 12992w3 [0,0,0,-17324,877648] 2 12992w4 [0,0,0,-524,27792] 2
12992x (2 curves)	0	2- 7+ 29+	2-  1  3 7+ -3  1  0 -4
Curve Equation t 12992x1 [0,1,0,-929,-108577] 1 12992x2 [0,1,0,8351,2899999] 1
12992y (1 curve)	2	2- 7+ 29+	2- -1 -1 7+ -5  5 -4 -4
Curve Equation t Generators 12992y1 [0,-1,0,-1,929] 1 [-5:28:1]&[5:32:1]
12992z (2 curves)	1	2- 7+ 29-	2-  0  4 7+ -4  4  0 -4
Curve Equation t Generators 12992z1 [0,0,0,-68,-320] 2 [60:460:1] 12992z2 [0,0,0,-1228,-16560] 2 [8080:52164:125]
12992ba (1 curve)	1	2- 7+ 29-	2- -1  1 7+  1 -1  2 -4
Curve Equation t Generators 12992ba1 [0,-1,0,-145,-1711] 1 [55:392:1]
12992bb (2 curves)	1	2- 7+ 29-	2- -1  4 7+  2 -4 -2  5
Curve Equation t Generators 12992bb1 [0,-1,0,79,-17] 1 [42:275:1] 12992bb2 [0,-1,0,-8601,309943] 1 [42:145:1]
12992bc (2 curves)	1	2- 7+ 29-	2-  2  0 7+  0 -4  2  6
Curve Equation t Generators 12992bc1 [0,-1,0,-8513,-355231] 2 [300475:8836416:343] 12992bc2 [0,-1,0,-143073,-20781439] 2 [227819529:6147077336:250047]
12992bd (2 curves)	1	2- 7+ 29-	2-  2 -2 7+  4  2 -4  2
Curve Equation t Generators 12992bd1 [0,-1,0,-135969,30615233] 2 [5857461:79754176:19683] 12992bd2 [0,-1,0,-2511649,1532520129] 2 [16747932379221:11073350282176:17964142659]
12992be (2 curves)	1	2- 7+ 29-	2-  2 -2 7+ -4  2  4  2
Curve Equation t Generators 12992be1 [0,-1,0,-609,-5887] 2 [9309:172144:27] 12992be2 [0,-1,0,-9889,-375231] 2 [3247419:57946384:9261]
12992bf (2 curves)	1	2- 7+ 29-	2- -2  2 7+  0 -2  0  6
Curve Equation t Generators 12992bf1 [0,1,0,303,-2513] 2 [9:32:1] 12992bf2 [0,1,0,-2017,-27105] 2 [241:3680:1]
12992bg (1 curve)	1	2- 7+ 29-	2- -3  1 7+ -1  7 -6 -4
Curve Equation t Generators 12992bg1 [0,0,0,533,1528] 1 [284:4802:1]
12992bh (1 curve)	1	2- 7- 29+	2- -1  3 7- -1  1 -4 -4
Curve Equation t Generators 12992bh1 [0,-1,0,-6529,-201439] 1 [245:3584:1]
12992bi (2 curves)	0	2- 7- 29-	2-  0  0 7- -4  0 -4  4
Curve Equation t 12992bi1 [0,0,0,-19340,-1118448] 2 12992bi2 [0,0,0,-316300,-68468976] 2
12992bj (2 curves)	0	2- 7- 29-	2-  0  4 7-  4  4  0  4
Curve Equation t 12992bj1 [0,0,0,-68,320] 2 12992bj2 [0,0,0,-1228,16560] 2
12992bk (1 curve)	0	2- 7- 29-	2-  1  0 7- -6 -4  6 -5
Curve Equation t 12992bk1 [0,1,0,27,-61] 1
12992bl (2 curves)	0	2- 7- 29-	2-  2 -2 7-  0 -6  4  2
Curve Equation t 12992bl1 [0,-1,0,-29,29] 2 12992bl2 [0,-1,0,111,113] 2
12992bm (1 curve)	0	2- 7- 29-	2-  3  0 7-  2  0  2  1
Curve Equation t 12992bm1 [0,0,0,-160,992] 1
12992bn (1 curve)	0	2- 7- 29-	2-  3  1 7-  1  7 -6  4
Curve Equation t 12992bn1 [0,0,0,533,-1528] 1

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations