Cremona's table of elliptic curves

31584 = 2⁵ · 3 · 7 · 47

Class	r	Atkin-Lehner	Eigenvalues
31584a (2 curves)	0	2+ 3+ 7+ 47-	2+ 3+  0 7+ -2  4 -2  4
Curve Equation t 31584a1 [0,-1,0,-5038,193120] 2 31584a2 [0,-1,0,-89073,10260513] 2
31584b (1 curve)	0	2+ 3+ 7+ 47-	2+ 3+  0 7+ -5 -2  7  1
Curve Equation t 31584b1 [0,-1,0,-173,-1179] 1
31584c (2 curves)	0	2+ 3+ 7+ 47-	2+ 3+  4 7+ -4  2 -6 -2
Curve Equation t 31584c1 [0,-1,0,14,-392] 2 31584c2 [0,-1,0,-721,-7007] 2
31584d (2 curves)	0	2+ 3+ 7- 47+	2+ 3+  0 7-  6  4 -6  0
Curve Equation t 31584d1 [0,-1,0,42,-144] 2 31584d2 [0,-1,0,-273,-1215] 2
31584e (2 curves)	0	2+ 3+ 7- 47+	2+ 3+  2 7- -4  4  0 -4
Curve Equation t 31584e1 [0,-1,0,-1233582,-526940460] 2 31584e2 [0,-1,0,-1235297,-525400047] 2
31584f (2 curves)	0	2+ 3+ 7- 47+	2+ 3+  4 7-  2  0 -6  8
Curve Equation t 31584f1 [0,-1,0,-83286,9302688] 2 31584f2 [0,-1,0,-1333521,593162433] 2
31584g (2 curves)	1	2+ 3+ 7- 47-	2+ 3+  2 7-  0  2 -6  6
Curve Equation t Generators 31584g1 [0,-1,0,-2042,37128] 2 [11:126:1] 31584g2 [0,-1,0,-32912,2309160] 2 [109:70:1]
31584h (2 curves)	1	2+ 3+ 7- 47-	2+ 3+  2 7-  0 -4  0  0
Curve Equation t Generators 31584h1 [0,-1,0,-302,1380] 2 [22:70:1] 31584h2 [0,-1,0,-2017,-33263] 2 [-27:28:1]
31584i (1 curve)	1	2+ 3+ 7- 47-	2+ 3+ -4 7- -3  2 -3 -3
Curve Equation t Generators 31584i1 [0,-1,0,35,661] 1 [3:-28:1]
31584j (2 curves)	1	2+ 3- 7+ 47-	2+ 3-  0 7+ -6  4 -6  0
Curve Equation t Generators 31584j1 [0,1,0,42,144] 2 [0:12:1] 31584j2 [0,1,0,-273,1215] 2 [21:72:1]
31584k (2 curves)	1	2+ 3- 7+ 47-	2+ 3-  4 7+ -2  0 -6 -8
Curve Equation t Generators 31584k1 [0,1,0,-83286,-9302688] 2 [408:4980:1] 31584k2 [0,1,0,-1333521,-593162433] 2 [467745:27049368:125]
31584l (2 curves)	1	2+ 3- 7- 47+	2+ 3-  0 7-  2  4 -2 -4
Curve Equation t Generators 31584l1 [0,1,0,-5038,-193120] 2 [1457:55566:1] 31584l2 [0,1,0,-89073,-10260513] 2 [-174:21:1]
31584m (1 curve)	1	2+ 3- 7- 47+	2+ 3-  0 7-  5 -2  7 -1
Curve Equation t Generators 31584m1 [0,1,0,-173,1179] 1 [13:36:1]
31584n (2 curves)	0	2+ 3- 7- 47-	2+ 3-  2 7- -4  6  2  2
Curve Equation t 31584n1 [0,1,0,-362,-3168] 2 31584n2 [0,1,0,-6032,-182340] 2
31584o (2 curves)	0	2- 3+ 7+ 47+	2- 3+  0 7+ -6  0 -2  6
Curve Equation t 31584o1 [0,-1,0,-278,-2040] 2 31584o2 [0,-1,0,-4688,-121992] 2
31584p (2 curves)	0	2- 3+ 7+ 47+	2- 3+  2 7+  4  6  2 -2
Curve Equation t 31584p1 [0,-1,0,-362,3168] 2 31584p2 [0,-1,0,-6032,182340] 2
31584q (2 curves)	0	2- 3+ 7- 47-	2- 3+  0 7-  0  6  2 -4
Curve Equation t 31584q1 [0,-1,0,2,-56] 2 31584q2 [0,-1,0,-208,-1064] 2
31584r (4 curves)	0	2- 3+ 7- 47-	2- 3+  2 7-  4  2  6  4
Curve Equation t 31584r1 [0,-1,0,-862,-8840] 4 31584r2 [0,-1,0,783,-40095] 2 31584r3 [0,-1,0,-2752,45592] 2 31584r4 [0,-1,0,-13552,-602732] 2
31584s (2 curves)	0	2- 3+ 7- 47-	2- 3+  4 7- -2  0 -2  2
Curve Equation t 31584s1 [0,-1,0,-95046,-26594712] 2 31584s2 [0,-1,0,-2039856,-1119577932] 2
31584t (2 curves)	1	2- 3- 7+ 47+	2- 3-  0 7+  0  6  2  4
Curve Equation t Generators 31584t1 [0,1,0,2,56] 2 [4:12:1] 31584t2 [0,1,0,-208,1064] 2 [74:33:8]
31584u (2 curves)	1	2- 3- 7+ 47+	2- 3-  2 7+  0  2 -6 -6
Curve Equation t Generators 31584u1 [0,1,0,-2042,-37128] 2 [652:16620:1] 31584u2 [0,1,0,-32912,-2309160] 2 [662290:16334967:1000]
31584v (2 curves)	1	2- 3- 7+ 47+	2- 3-  2 7+  0 -4  0  0
Curve Equation t Generators 31584v1 [0,1,0,-302,-1380] 2 [-1074:1045:216] 31584v2 [0,1,0,-2017,33263] 2 [2:171:1]
31584w (4 curves)	1	2- 3- 7+ 47+	2- 3-  2 7+ -4  2  6 -4
Curve Equation t Generators 31584w1 [0,1,0,-862,8840] 4 [38:180:1] 31584w2 [0,1,0,783,40095] 2 [-9:180:1] 31584w3 [0,1,0,-2752,-45592] 2 [59:30:1] 31584w4 [0,1,0,-13552,602732] 2 [586:735:8]
31584x (2 curves)	1	2- 3- 7+ 47+	2- 3-  4 7+  2  0 -2 -2
Curve Equation t Generators 31584x1 [0,1,0,-95046,26594712] 2 [273:4590:1] 31584x2 [0,1,0,-2039856,1119577932] 2 [106155:83946:125]
31584y (1 curve)	1	2- 3- 7+ 47+	2- 3- -4 7+  3  2 -3  3
Curve Equation t Generators 31584y1 [0,1,0,35,-661] 1 [49:348:1]
31584z (2 curves)	0	2- 3- 7+ 47-	2- 3-  2 7+  4  4  0  4
Curve Equation t 31584z1 [0,1,0,-1233582,526940460] 2 31584z2 [0,1,0,-1235297,525400047] 2
31584ba (2 curves)	0	2- 3- 7- 47+	2- 3-  4 7-  4  2 -6  2
Curve Equation t 31584ba1 [0,1,0,14,392] 2 31584ba2 [0,1,0,-721,7007] 2
31584bb (2 curves)	1	2- 3- 7- 47-	2- 3-  0 7-  6  0 -2 -6
Curve Equation t Generators 31584bb1 [0,1,0,-278,2040] 2 [1:42:1] 31584bb2 [0,1,0,-4688,121992] 2 [43:42:1]

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