Cremona's table of elliptic curves

34080 = 2⁵ · 3 · 5 · 71

Class	r	Atkin-Lehner	Eigenvalues
34080a (2 curves)	1	2+ 3+ 5+ 71+	2+ 3+ 5+  0  2  2  2 -4
Curve Equation t Generators 34080a1 [0,-1,0,14,40] 2 [3:10:1] 34080a2 [0,-1,0,-136,580] 2 [9:2:1]
34080b (1 curve)	1	2+ 3+ 5+ 71+	2+ 3+ 5+  3  2  5 -2 -5
Curve Equation t Generators 34080b1 [0,-1,0,4339,-290139] 1 [68:561:1]
34080c (1 curve)	1	2+ 3+ 5+ 71+	2+ 3+ 5+ -3  2 -1  2 -1
Curve Equation t Generators 34080c1 [0,-1,0,-587581,-173164619] 1 [126314:15852453:8]
34080d (2 curves)	1	2+ 3+ 5+ 71+	2+ 3+ 5+ -4  2  4 -6  4
Curve Equation t Generators 34080d1 [0,-1,0,-1326,20160] 2 [8:100:1] 34080d2 [0,-1,0,-21576,1227060] 2 [84:18:1]
34080e (2 curves)	0	2+ 3+ 5+ 71-	2+ 3+ 5+  0  2 -4 -2  4
Curve Equation t 34080e1 [0,-1,0,85554,6538320] 2 34080e2 [0,-1,0,-420696,57973320] 2
34080f (2 curves)	2	2+ 3+ 5+ 71-	2+ 3+ 5+  2 -2 -6 -8  8
Curve Equation t Generators 34080f1 [0,-1,0,-6,-144] 2 [8:16:1]&[15:54:1] 34080f2 [0,-1,0,-456,-3564] 2 [-12:6:1]&[53:344:1]
34080g (2 curves)	2	2+ 3+ 5+ 71-	2+ 3+ 5+ -2 -2  2 -4 -8
Curve Equation t Generators 34080g1 [0,-1,0,-168726,26744976] 2 [-232:7304:1]&[174:1620:1] 34080g2 [0,-1,0,-2699976,1708507476] 2 [-420:52614:1]&[948:54:1]
34080h (1 curve)	2	2+ 3+ 5+ 71-	2+ 3+ 5+ -5 -2 -1  2  1
Curve Equation t Generators 34080h1 [0,-1,0,19,165] 1 [-4:3:1]&[-1:12:1]
34080i (4 curves)	0	2+ 3+ 5- 71+	2+ 3+ 5-  0 -4  2 -2  4
Curve Equation t 34080i1 [0,-1,0,-3930,23400] 4 34080i2 [0,-1,0,15240,169092] 2 34080i3 [0,-1,0,-37680,-2784600] 2 34080i4 [0,-1,0,-48305,4097025] 2
34080j (2 curves)	0	2+ 3+ 5- 71+	2+ 3+ 5- -2  2  4  0  4
Curve Equation t 34080j1 [0,-1,0,430,1800] 2 34080j2 [0,-1,0,-2000,17352] 2
34080k (2 curves)	1	2+ 3+ 5- 71-	2+ 3+ 5- -2  0  2  4 -8
Curve Equation t Generators 34080k1 [0,-1,0,70,72] 2 [4:20:1] 34080k2 [0,-1,0,-305,897] 2 [19:40:1]
34080l (2 curves)	1	2+ 3+ 5- 71-	2+ 3+ 5- -4  4 -4 -6  0
Curve Equation t Generators 34080l1 [0,-1,0,50,400] 2 [0:20:1] 34080l2 [0,-1,0,-625,5665] 2 [27:88:1]
34080m (2 curves)	0	2+ 3- 5+ 71+	2+ 3- 5+  0 -2 -4 -2 -4
Curve Equation t 34080m1 [0,1,0,85554,-6538320] 2 34080m2 [0,1,0,-420696,-57973320] 2
34080n (2 curves)	0	2+ 3- 5+ 71+	2+ 3- 5+  2  2  2 -4  8
Curve Equation t 34080n1 [0,1,0,-168726,-26744976] 2 34080n2 [0,1,0,-2699976,-1708507476] 2
34080o (2 curves)	0	2+ 3- 5+ 71+	2+ 3- 5+  2 -2  4 -4 -4
Curve Equation t 34080o1 [0,1,0,-426,-4176] 2 34080o2 [0,1,0,-7176,-236376] 2
34080p (2 curves)	0	2+ 3- 5+ 71+	2+ 3- 5+ -2  2  0  8 -4
Curve Equation t 34080p1 [0,1,0,-239029146,1424725490304] 2 34080p2 [0,1,0,-3826255896,91096784896104] 2
34080q (2 curves)	2	2+ 3- 5+ 71+	2+ 3- 5+ -2  2 -6 -8 -8
Curve Equation t Generators 34080q1 [0,1,0,-6,144] 2 [-3:12:1]&[0:12:1] 34080q2 [0,1,0,-456,3564] 2 [15:18:1]&[27:108:1]
34080r (2 curves)	0	2+ 3- 5+ 71+	2+ 3- 5+ -2  6  4  0  4
Curve Equation t 34080r1 [0,1,0,-26,240] 2 34080r2 [0,1,0,-776,8040] 2
34080s (1 curve)	0	2+ 3- 5+ 71+	2+ 3- 5+  5  2 -1  2 -1
Curve Equation t 34080s1 [0,1,0,19,-165] 1
34080t (1 curve)	1	2+ 3- 5+ 71-	2+ 3- 5+ -3 -2  5 -2  5
Curve Equation t Generators 34080t1 [0,1,0,4339,290139] 1 [57:852:1]
34080u (2 curves)	1	2+ 3- 5+ 71-	2+ 3- 5+  4 -2  4 -6 -4
Curve Equation t Generators 34080u1 [0,1,0,-1326,-20160] 2 [96:864:1] 34080u2 [0,1,0,-21576,-1227060] 2 [171:336:1]
34080v (2 curves)	1	2+ 3- 5- 71+	2+ 3- 5-  4 -4 -4 -6  0
Curve Equation t Generators 34080v1 [0,1,0,50,-400] 2 [8:24:1] 34080v2 [0,1,0,-625,-5665] 2 [53:336:1]
34080w (1 curve)	1	2- 3+ 5+ 71-	2- 3+ 5+  1  6  1 -2 -3
Curve Equation t Generators 34080w1 [0,-1,0,-11981,814725] 1 [500:10935:1]
34080x (2 curves)	1	2- 3+ 5+ 71-	2- 3+ 5+  2 -2  0  8  4
Curve Equation t Generators 34080x1 [0,-1,0,-239029146,-1424725490304] 2 [10829748599349502241887070638:-928996975193624529271738744436:502939184441079331477511] 34080x2 [0,-1,0,-3826255896,-91096784896104] 2 [-252232238651426478467285693438333730622712033779824693405790:-3817286365794662223623053306598277130122255926631058635817:7062871997488182984756300044168602800220344401068354408]
34080y (2 curves)	1	2- 3+ 5+ 71-	2- 3+ 5+  2 -6  4  0 -4
Curve Equation t Generators 34080y1 [0,-1,0,-26,-240] 2 [10:20:1] 34080y2 [0,-1,0,-776,-8040] 2 [85:730:1]
34080z (2 curves)	1	2- 3+ 5+ 71-	2- 3+ 5+ -2  2  4 -4  4
Curve Equation t Generators 34080z1 [0,-1,0,-426,4176] 2 [3:54:1] 34080z2 [0,-1,0,-7176,236376] 2 [53:46:1]
34080ba (4 curves)	0	2- 3+ 5- 71-	2- 3+ 5-  0  4  6  6  0
Curve Equation t 34080ba1 [0,-1,0,-1950,-30600] 4 34080ba2 [0,-1,0,1600,-132840] 2 34080ba3 [0,-1,0,-6000,142740] 4 34080ba4 [0,-1,0,-30705,-2060703] 2
34080bb (2 curves)	2	2- 3+ 5- 71-	2- 3+ 5- -2 -6 -2  4  0
Curve Equation t Generators 34080bb1 [0,-1,0,130,1032] 2 [-1:30:1]&[2:36:1] 34080bb2 [0,-1,0,-1120,12532] 2 [-36:70:1]&[4:90:1]
34080bc (1 curve)	1	2- 3- 5+ 71+	2- 3- 5+ -1 -6  1 -2  3
Curve Equation t Generators 34080bc1 [0,1,0,-11981,-814725] 1 [229:-2916:1]
34080bd (2 curves)	0	2- 3- 5+ 71-	2- 3- 5+  0 -2  2  2  4
Curve Equation t 34080bd1 [0,1,0,14,-40] 2 34080bd2 [0,1,0,-136,-580] 2
34080be (1 curve)	0	2- 3- 5+ 71-	2- 3- 5+  3 -2 -1  2  1
Curve Equation t 34080be1 [0,1,0,-587581,173164619] 1
34080bf (4 curves)	0	2- 3- 5- 71+	2- 3- 5-  0 -4  6  6  0
Curve Equation t 34080bf1 [0,1,0,-1950,30600] 4 34080bf2 [0,1,0,1600,132840] 2 34080bf3 [0,1,0,-6000,-142740] 2 34080bf4 [0,1,0,-30705,2060703] 4
34080bg (2 curves)	0	2- 3- 5- 71+	2- 3- 5-  2  0  2  4  8
Curve Equation t 34080bg1 [0,1,0,70,-72] 2 34080bg2 [0,1,0,-305,-897] 2
34080bh (2 curves)	0	2- 3- 5- 71+	2- 3- 5-  2  6 -2  4  0
Curve Equation t 34080bh1 [0,1,0,130,-1032] 2 34080bh2 [0,1,0,-1120,-12532] 2
34080bi (4 curves)	1	2- 3- 5- 71-	2- 3- 5-  0  4  2 -2 -4
Curve Equation t Generators 34080bi1 [0,1,0,-3930,-23400] 4 [-15:180:1] 34080bi2 [0,1,0,15240,-169092] 2 [411:8700:1] 34080bi3 [0,1,0,-37680,2784600] 2 [-165:2130:1] 34080bi4 [0,1,0,-48305,-4097025] 2 [-125:60:1]
34080bj (2 curves)	1	2- 3- 5- 71-	2- 3- 5-  2 -2  4  0 -4
Curve Equation t Generators 34080bj1 [0,1,0,430,-1800] 2 [10:60:1] 34080bj2 [0,1,0,-2000,-17352] 2 [-14:90:1]

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