Cremona's table of elliptic curves

80223 = 3 · 11² · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
80223a (1 curve)	1	3+ 11+ 13+ 17+	0 3+  2  5 11+ 13+ 17+ -4
Curve Equation t Generators 80223a1 [0,-1,1,103,2474] 1 [26:148:1]
80223b (1 curve)	1	3+ 11+ 13- 17-	0 3+  2 -5 11+ 13- 17-  4
Curve Equation t Generators 80223b1 [0,-1,1,12423,-3342967] 1 [123:175:1]
80223c (6 curves)	0	3+ 11- 13+ 17+	1 3+ -2  0 11- 13+ 17+  4
Curve Equation t 80223c1 [1,1,0,-65221,-6438296] 2 80223c2 [1,1,0,-65826,-6313545] 4 80223c3 [1,1,0,26739,-22549446] 2 80223c4 [1,1,0,-168071,17918520] 4 80223c5 [1,1,0,468994,122014941] 2 80223c6 [1,1,0,-2441056,1466719159] 2
80223d (2 curves)	0	3+ 11- 13+ 17+	-1 3+  0  4 11- 13+ 17+  2
Curve Equation t 80223d1 [1,1,1,-13373,584090] 2 80223d2 [1,1,1,-3088,1472714] 2
80223e (1 curve)	0	3+ 11- 13+ 17+	-1 3+  3 -2 11- 13+ 17+  4
Curve Equation t 80223e1 [1,1,1,1026,29184] 1
80223f (1 curve)	2	3+ 11- 13+ 17+	-2 3+  0  1 11- 13+ 17+ -1
Curve Equation t Generators 80223f1 [0,-1,1,-2218,273360] 1 [-75:110:1]&[81:786:1]
80223g (2 curves)	1	3+ 11- 13+ 17-	1 3+  0  0 11- 13+ 17- -6
Curve Equation t Generators 80223g1 [1,1,0,-50691940015,-937825931943248] 2 [-125004321215988036:-88042718625341863043:5028334923968] 80223g2 [1,1,0,197562957150,-7411866791191551] 2 [22835092264271363634206740:-64465552671727742511354694433:2875136541170890816]
80223h (2 curves)	1	3+ 11- 13- 17+	-1 3+ -4 -2 11- 13- 17+ -4
Curve Equation t Generators 80223h1 [1,1,1,-31765,2163866] 2 [-16:1641:1] 80223h2 [1,1,1,-39630,999846] 2 [-29:1472:1]
80223i (1 curve)	0	3+ 11- 13- 17-	1 3+  3  2 11- 13- 17- -4
Curve Equation t 80223i1 [1,1,0,9,-18] 1
80223j (1 curve)	0	3+ 11- 13- 17-	2 3+  0 -1 11- 13- 17-  1
Curve Equation t 80223j1 [0,-1,1,-18,-199] 1
80223k (1 curve)	1	3- 11- 13+ 17+	1 3-  3 -2 11- 13+ 17+  4
Curve Equation t Generators 80223k1 [1,0,1,1049188,608136923] 1 [-111:22198:1]
80223l (1 curve)	1	3- 11- 13+ 17+	2 3- -2 -3 11- 13+ 17+ -1
Curve Equation t Generators 80223l1 [0,1,1,-209854,-121518809] 1 [29123104:651071495:32768]
80223m (1 curve)	0	3- 11- 13+ 17-	1 3-  1  0 11- 13+ 17- -8
Curve Equation t 80223m1 [1,0,1,-110113,15232325] 1
80223n (4 curves)	0	3- 11- 13+ 17-	1 3-  2  0 11- 13+ 17- -4
Curve Equation t 80223n1 [1,0,1,74775,5309599] 2 80223n2 [1,0,1,-366270,46591411] 4 80223n3 [1,0,1,-2702175,-1677306479] 2 80223n4 [1,0,1,-5087085,4414289449] 2
80223o (2 curves)	0	3- 11- 13- 17+	1 3-  0  2 11- 13- 17+  0
Curve Equation t 80223o1 [1,0,1,-3996,91837] 2 80223o2 [1,0,1,-11861,-383209] 2
80223p (1 curve)	0	3- 11- 13- 17+	-1 3-  1  0 11- 13- 17+  8
Curve Equation t 80223p1 [1,0,0,-910,-11527] 1
80223q (1 curve)	1	3- 11- 13- 17-	-1 3-  3  2 11- 13- 17- -4
Curve Equation t Generators 80223q1 [1,0,0,8671,-456114] 1 [55:406:1]
80223r (1 curve)	1	3- 11- 13- 17-	-2 3- -2  3 11- 13- 17-  1
Curve Equation t Generators 80223r1 [0,1,1,-1734,90668] 1 [-12:331:1]

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

Part of Computational Number Theory
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