Cremona's table of elliptic curves

33072 = 2⁴ · 3 · 13 · 53

Class	r	Atkin-Lehner	Eigenvalues
33072a (1 curve)	1	2+ 3+ 13+ 53+	2+ 3+  2 -2  5 13+  0  5
Curve Equation t Generators 33072a1 [0,-1,0,23,5557] 1 [-204:1889:27]
33072b (2 curves)	2	2+ 3+ 13+ 53-	2+ 3+  0 -4 -6 13+  2  0
Curve Equation t Generators 33072b1 [0,-1,0,2077,12714] 2 [30:318:1]&[2110:96922:1] 33072b2 [0,-1,0,-8908,113776] 2 [172:-1908:1]&[12:92:1]
33072c (1 curve)	0	2+ 3+ 13- 53+	2+ 3+  2 -3  3 13- -4 -5
Curve Equation t 33072c1 [0,-1,0,5648,46048] 1
33072d (1 curve)	1	2+ 3+ 13- 53-	2+ 3+  0  0 -5 13-  6 -1
Curve Equation t Generators 33072d1 [0,-1,0,-33,93] 1 [4:3:1]
33072e (6 curves)	1	2+ 3+ 13- 53-	2+ 3+ -2  0  4 13-  2  4
Curve Equation t Generators 33072e1 [0,-1,0,-22399,-697970] 2 [-78:754:1] 33072e2 [0,-1,0,-165204,25406784] 4 [3770:57681:8] 33072e3 [0,-1,0,13936,77429040] 2 [1954602:63788777:5832] 33072e4 [0,-1,0,-2629224,1641803904] 8 [355903002:362534780322:343] 33072e5 [0,-1,0,-2615184,1660190688] 4 [14511240899722:-86704717574745:15289924168] 33072e6 [0,-1,0,-42067584,105033408480] 4 [18962931703295530:-660699130810473:5061868813000]
33072f (2 curves)	2	2+ 3- 13+ 53+	2+ 3- -2  0 -2 13+ -6 -6
Curve Equation t Generators 33072f1 [0,1,0,36,-84] 2 [11:42:1]&[38:240:1] 33072f2 [0,1,0,-224,-1020] 2 [-8:18:1]&[-6:12:1]
33072g (1 curve)	2	2+ 3- 13+ 53+	2+ 3- -2 -3 -5 13+  0 -3
Curve Equation t Generators 33072g1 [0,1,0,-260744,51160980] 1 [298:108:1]&[-332:10062:1]
33072h (1 curve)	1	2+ 3- 13- 53+	2+ 3- -3 -2 -1 13-  3  6
Curve Equation t Generators 33072h1 [0,1,0,-389032,93308564] 1 [380:-702:1]
33072i (2 curves)	0	2+ 3- 13- 53-	2+ 3-  0  4  4 13-  6  6
Curve Equation t 33072i1 [0,1,0,-163,-856] 2 33072i2 [0,1,0,-228,-180] 2
33072j (1 curve)	0	2- 3+ 13+ 53+	2- 3+  2  2 -5 13+  0  7
Curve Equation t 33072j1 [0,-1,0,83,97] 1
33072k (1 curve)	2	2- 3+ 13+ 53+	2- 3+ -2  1 -5 13+ -8  7
Curve Equation t Generators 33072k1 [0,-1,0,-144,8640] 1 [-22:26:1]&[-8:96:1]
33072l (2 curves)	1	2- 3+ 13+ 53-	2- 3+  2  4  2 13+  2 -2
Curve Equation t Generators 33072l1 [0,-1,0,-632,25200] 2 [-54:1365:8] 33072l2 [0,-1,0,-17272,877168] 2 [316:5184:1]
33072m (1 curve)	1	2- 3+ 13+ 53-	2- 3+ -2 -2  3 13+  0 -7
Curve Equation t Generators 33072m1 [0,-1,0,-2629,-51155] 1 [164628:2398051:729]
33072n (2 curves)	1	2- 3+ 13+ 53-	2- 3+ -2 -2 -6 13+ -2 -2
Curve Equation t Generators 33072n1 [0,-1,0,-12169,520768] 2 [48:212:1] 33072n2 [0,-1,0,-12124,524764] 2 [85:-318:1]
33072o (2 curves)	1	2- 3+ 13- 53+	2- 3+  0  4 -3 13-  6  7
Curve Equation t Generators 33072o1 [0,-1,0,-213,5661] 1 [-20:39:1] 33072o2 [0,-1,0,-31413,2153469] 1 [-116:2055:1]
33072p (1 curve)	1	2- 3+ 13- 53+	2- 3+  1  2 -1 13- -1 -2
Curve Equation t Generators 33072p1 [0,-1,0,-1560,-24336] 1 [156:1872:1]
33072q (1 curve)	0	2- 3+ 13- 53-	2- 3+ -1  2  3 13-  3  2
Curve Equation t 33072q1 [0,-1,0,78864,580032] 1
33072r (2 curves)	0	2- 3+ 13- 53-	2- 3+  2  2  0 13- -6 -4
Curve Equation t 33072r1 [0,-1,0,-4297,-106628] 2 33072r2 [0,-1,0,-68692,-6906740] 2
33072s (4 curves)	0	2- 3+ 13- 53-	2- 3+  2 -4  0 13-  2  4
Curve Equation t 33072s1 [0,-1,0,-2152,-37520] 2 33072s2 [0,-1,0,-3432,13680] 4 33072s3 [0,-1,0,13528,95088] 2 33072s4 [0,-1,0,-40872,3188592] 4
33072t (2 curves)	1	2- 3- 13+ 53+	2- 3-  2  0 -2 13+  2 -2
Curve Equation t Generators 33072t1 [0,1,0,-46392,3964500] 2 [6:1920:1] 33072t2 [0,1,0,-749432,249466068] 2 [22:15264:1]
33072u (2 curves)	0	2- 3- 13+ 53-	2- 3-  0  2 -6 13+  2  4
Curve Equation t 33072u1 [0,1,0,-333,-2430] 2 33072u2 [0,1,0,-68,-5928] 2
33072v (2 curves)	0	2- 3- 13+ 53-	2- 3-  0 -2  2 13+  2  0
Curve Equation t 33072v1 [0,1,0,-573,-3258] 2 33072v2 [0,1,0,1812,-21384] 2
33072w (1 curve)	0	2- 3- 13- 53+	2- 3-  3  4  5 13-  5 -2
Curve Equation t 33072w1 [0,1,0,-2856664,1876003604] 1
33072x (2 curves)	1	2- 3- 13- 53-	2- 3- -2  2  4 13- -6  4
Curve Equation t Generators 33072x1 [0,1,0,-1209,-10170] 2 [-18:78:1] 33072x2 [0,1,0,-8364,284616] 2 [111:858:1]

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