Cremona's table of elliptic curves

8217 = 3² · 11 · 83

Class	r	Atkin-Lehner	Eigenvalues
8217a (1 curve)	1	3+ 11+ 83+	2 3+ -1  4 11+ -2 -1 -3
Curve Equation t Generators 8217a1 [0,0,1,117,-395] 1 [82:343:8]
8217b (2 curves)	0	3+ 11+ 83-	-1 3+  0  2 11+ -2  6  2
Curve Equation t 8217b1 [1,-1,1,-42635,-3377726] 2 8217b2 [1,-1,1,-42770,-3355154] 2
8217c (2 curves)	0	3+ 11- 83+	1 3+  0  2 11- -2 -6  2
Curve Equation t 8217c1 [1,-1,0,-4737,126680] 2 8217c2 [1,-1,0,-4752,125849] 2
8217d (1 curve)	1	3+ 11- 83-	-2 3+  1  4 11- -2  1 -3
Curve Equation t Generators 8217d1 [0,0,1,1053,10658] 1 [-8:41:1]
8217e (1 curve)	2	3- 11+ 83+	0 3- -3 -2 11+ -2  3 -1
Curve Equation t Generators 8217e1 [0,0,1,6,-68] 1 [4:4:1]&[10:31:1]
8217f (2 curves)	1	3- 11+ 83-	1 3- -4  0 11+  0 -2  2
Curve Equation t Generators 8217f1 [1,-1,0,-6489,201784] 2 [56:80:1] 8217f2 [1,-1,0,-2754,429619] 2 [-50:5371:8]
8217g (4 curves)	1	3- 11+ 83-	-1 3- -2 -4 11+  2  2 -4
Curve Equation t Generators 8217g1 [1,-1,1,-21416,-1060158] 4 [170:351:1] 8217g2 [1,-1,1,-331421,-73353324] 4 [20837:2996193:1] 8217g3 [1,-1,1,-5302706,-4698636888] 2 [11516031374:1647940750827:551368] 8217g4 [1,-1,1,-320216,-78552444] 2 [457411500:65772759989:21952]
8217h (1 curve)	1	3- 11+ 83-	-1 3- -4  1 11+  7 -4 -6
Curve Equation t Generators 8217h1 [1,-1,1,-139847,-288043680] 1 [1460:50439:1]
8217i (1 curve)	1	3- 11- 83+	1 3-  0 -1 11-  1  0  2
Curve Equation t Generators 8217i1 [1,-1,0,-1032,13877] 1 [4:97:1]
8217j (4 curves)	1	3- 11- 83+	-1 3-  2  0 11- -6  6  4
Curve Equation t Generators 8217j1 [1,-1,1,-1544,23730] 2 [35:90:1] 8217j2 [1,-1,1,-1589,22308] 4 [161:1899:1] 8217j3 [1,-1,1,-6044,-155892] 2 [1342:14355:8] 8217j4 [1,-1,1,2146,108960] 2 [-25:210:1]
8217k (1 curve)	1	3- 11- 83+	-2 3- -3 -4 11- -2  6  2
Curve Equation t Generators 8217k1 [0,0,1,-9,-358] 1 [13:41:1]
8217l (2 curves)	0	3- 11- 83-	-1 3-  4  2 11-  2 -4  8
Curve Equation t 8217l1 [1,-1,1,-21443,1209354] 2 8217l2 [1,-1,1,-32378,-146586] 2
8217m (1 curve)	2	3- 11- 83-	-2 3- -1  0 11- -6 -5 -7
Curve Equation t Generators 8217m1 [0,0,1,-1083,13900] 1 [-35:94:1]&[-8:148:1]

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