Cremona's table of elliptic curves

27209 = 7 · 13² · 23

Class	r	Atkin-Lehner	Eigenvalues
27209a (2 curves)	1	7+ 13+ 23+	0  1  3 7+ -3 13+  6  1
Curve Equation t Generators 27209a1 [0,1,1,-7383159,7719213259] 1 [-2999:53826:1] 27209a2 [0,1,1,-6965729,8630952880] 1 [-58668840:1063713592:19683]
27209b (3 curves)	1	7+ 13+ 23+	0  1 -3 7+  3 13+ -6  7
Curve Equation t Generators 27209b1 [0,1,1,2739603,1870924150] 1 [1311200:98948919:1331] 27209b2 [0,1,1,-26963837,-83903328245] 1 [1096889541:-188556895952:35937] 27209b3 [0,1,1,-2506212427,-48292813035840] 1 [5222703478935317236373688:-276138007504365630002911489:88420461245029520937]
27209c (2 curves)	1	7+ 13+ 23+	0 -2  0 7+  3 13+ -3 -8
Curve Equation t Generators 27209c1 [0,1,1,-5633,148230] 1 [30:84:1] 27209c2 [0,1,1,-93513,-11010333] 1 [-4767:4465:27]
27209d (4 curves)	1	7+ 13+ 23+	1  0 -2 7+ -4 13+ -2 -4
Curve Equation t Generators 27209d1 [1,-1,0,-623,-5680] 2 [-8120:6505:512] 27209d2 [1,-1,0,-1468,13755] 4 [78:99:8] 27209d3 [1,-1,0,4447,93016] 2 [37934:2593235:8] 27209d4 [1,-1,0,-20903,1168194] 2 [114:450:1]
27209e (2 curves)	1	7+ 13+ 23+	1  2  0 7+  4 13+  8 -4
Curve Equation t Generators 27209e1 [1,1,0,2870,-57897] 2 [281468466554430:2093333180049677:9320662666125] 27209e2 [1,1,0,-16565,-567094] 2 [1100994978:8734826416:6128487]
27209f (1 curve)	1	7+ 13+ 23+	2 -1 -1 7+  3 13+  8  1
Curve Equation t Generators 27209f1 [0,-1,1,-56,-12777] 1 [826:8277:8]
27209g (1 curve)	0	7+ 13+ 23-	2 -1  3 7+ -1 13+  4  5
Curve Equation t 27209g1 [0,-1,1,-7154,235653] 1
27209h (1 curve)	0	7+ 13+ 23-	-2  2 -2 7+ -3 13+  1  4
Curve Equation t 27209h1 [0,-1,1,-30814,-2058184] 1
27209i (2 curves)	0	7+ 13- 23+	-2 -1 -3 7+  5 13-  2 -1
Curve Equation t 27209i1 [0,-1,1,284878,65606712] 1 27209i2 [0,-1,1,-62878872,191934744510] 1
27209j (1 curve)	1	7+ 13- 23-	0  0 -2 7+ -3 13- -3  4
Curve Equation t Generators 27209j1 [0,0,1,-26,42] 1 [0:6:1]
27209k (1 curve)	1	7+ 13- 23-	0 -3 -1 7+  1 13-  4  5
Curve Equation t Generators 27209k1 [0,0,1,-8788,1206702] 1 [0:1098:1]
27209l (1 curve)	0	7- 13+ 23+	0  2  4 7-  5 13+  3  4
Curve Equation t 27209l1 [0,-1,1,-604231,161682029] 1
27209m (1 curve)	1	7- 13+ 23-	0 -1 -1 7- -5 13+ -6  1
Curve Equation t Generators 27209m1 [0,-1,1,-901,16798] 1 [74:591:1]
27209n (1 curve)	1	7- 13+ 23-	2  3 -3 7- -3 13+  4 -5
Curve Equation t Generators 27209n1 [0,0,1,-258739,-70988915] 1 [252996102:9527345335:157464]
27209o (2 curves)	1	7- 13- 23+	2 -1  3 7- -5 13-  2  1
Curve Equation t Generators 27209o1 [0,-1,1,1686,29343] 1 [-118:255:8] 27209o2 [0,-1,1,-372064,87476677] 1 [2810:339:8]
27209p (1 curve)	0	7- 13- 23-	0  0  2 7-  3 13- -3 -4
Curve Equation t 27209p1 [0,0,1,-4394,92823] 1
27209q (1 curve)	2	7- 13- 23-	0 -3  1 7- -1 13-  4 -5
Curve Equation t Generators 27209q1 [0,0,1,-52,549] 1 [13:-46:1]&[34:157:8]

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