Cremona's table of elliptic curves

6171 = 3 · 11² · 17

Class	r	Atkin-Lehner	Eigenvalues
6171a (1 curve)	1	3+ 11- 17-	0 3+ -2  3 11- -2 17- -2
Curve Equation t Generators 6171a1 [0,-1,1,-451249,116824311] 1 [763:14701:1]
6171b (2 curves)	0	3- 11+ 17+	1 3-  0 -2 11+  0 17+  4
Curve Equation t 6171b1 [1,0,1,-14281,-220585] 2 6171b2 [1,0,1,-127416,17337967] 2
6171c (2 curves)	1	3- 11+ 17-	-1 3-  0  2 11+  0 17- -4
Curve Equation t Generators 6171c1 [1,0,0,-118,155] 2 [-7:29:1] 6171c2 [1,0,0,-1053,-13122] 2 [-18:18:1]
6171d (4 curves)	1	3- 11- 17+	1 3-  2  0 11-  2 17+ -8
Curve Equation t Generators 6171d1 [1,0,1,-1455,-21419] 2 [-25010600085:4927471777:1108717875] 6171d2 [1,0,1,-2060,-2059] 4 [511560:15899279:512] 6171d3 [1,0,1,-22025,1251743] 2 [10105:-759:125] 6171d4 [1,0,1,8225,-14401] 2 [31958:2004475:8]
6171e (1 curve)	1	3- 11- 17+	-2 3-  2 -3 11-  2 17+ -5
Curve Equation t Generators 6171e1 [0,1,1,-4572,-158416] 1 [342:-6197:1]
6171f (1 curve)	0	3- 11- 17-	0 3- -2 -1 11-  6 17-  6
Curve Equation t 6171f1 [0,1,1,-32589,-2297509] 1
6171g (2 curves)	0	3- 11- 17-	0 3-  3  4 11-  1 17-  1
Curve Equation t 6171g1 [0,1,1,81,1370] 1 6171g2 [0,1,1,-7179,231875] 1
6171h (1 curve)	0	3- 11- 17-	2 3-  0  3 11-  4 17-  2
Curve Equation t 6171h1 [0,1,1,-1008,-14965] 1
6171i (1 curve)	0	3- 11- 17-	2 3-  2  3 11- -2 17-  5
Curve Equation t 6171i1 [0,1,1,-553252,208638403] 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