Cremona's table of elliptic curves

12369 = 3 · 7 · 19 · 31

Class	r	Atkin-Lehner	Eigenvalues
12369a (1 curve)	0	3+ 7+ 19+ 31-	0 3+  2 7+ -2 -2  3 19+
Curve Equation t 12369a1 [0,-1,1,-288947,-59956747] 1
12369b (2 curves)	0	3+ 7+ 19+ 31-	1 3+  4 7+  6  4 -4 19+
Curve Equation t 12369b1 [1,1,0,-1143,-15360] 2 12369b2 [1,1,0,-1178,-14415] 2
12369c (1 curve)	2	3+ 7+ 19+ 31-	-2 3+  0 7+ -4  0  1 19+
Curve Equation t Generators 12369c1 [0,-1,1,-78,-340] 1 [11:3:1]&[15:40:1]
12369d (2 curves)	0	3- 7+ 19+ 31+	-1 3- -4 7+ -2  4  0 19+
Curve Equation t 12369d1 [1,0,0,-10144645,12405864776] 2 12369d2 [1,0,0,-14262360,1382741721] 2
12369e (4 curves)	1	3- 7+ 19+ 31-	-1 3- -2 7+  0  2  6 19+
Curve Equation t Generators 12369e1 [1,0,0,-132194,-18510765] 2 [631:11908:1] 12369e2 [1,0,0,-132199,-18509296] 4 [-211:149:1] 12369e3 [1,0,0,-144834,-14761755] 4 [-297:1590:1] 12369e4 [1,0,0,-119644,-22162801] 2 [626:11867:1]
12369f (1 curve)	1	3- 7+ 19+ 31-	2 3-  1 7+  0 -1 -6 19+
Curve Equation t Generators 12369f1 [0,1,1,0,23] 1 [58:167:8]
12369g (6 curves)	1	3- 7+ 19- 31+	-1 3- -2 7+ -4 -2  2 19-
Curve Equation t Generators 12369g1 [1,0,0,-1659,25848] 4 [-24:240:1] 12369g2 [1,0,0,-2064,12159] 8 [-6:159:1] 12369g3 [1,0,0,-18309,-946296] 4 [42744:1673048:27] 12369g4 [1,0,0,7701,96138] 4 [1254:17547:8] 12369g5 [1,0,0,-292194,-60817557] 2 [769483338:-29364883699:474552] 12369g6 [1,0,0,-4344,-2351175] 2 [138580379210:-1391286489559:753571000]
12369h (1 curve)	0	3- 7+ 19- 31-	2 3- -3 7+  0  7  2 19-
Curve Equation t 12369h1 [0,1,1,-11522,-488815] 1
12369i (2 curves)	1	3- 7- 19+ 31+	1 3- -2 7-  6  0  0 19+
Curve Equation t Generators 12369i1 [1,0,1,-372,-18515] 2 [35:90:1] 12369i2 [1,0,1,-13007,-569401] 2 [-69:61:1]
12369j (4 curves)	0	3- 7- 19+ 31-	1 3-  2 7-  4  2  2 19+
Curve Equation t 12369j1 [1,0,1,20,-91] 2 12369j2 [1,0,1,-225,-1169] 4 12369j3 [1,0,1,-3480,-79289] 2 12369j4 [1,0,1,-890,8939] 2
12369k (2 curves)	1	3- 7- 19- 31-	1 3-  0 7- -2  0  0 19-
Curve Equation t Generators 12369k1 [1,0,1,-1256,16577] 2 [310:1143:8] 12369k2 [1,0,1,-2971,-38989] 2 [163:1871:1]

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

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