Cremona's table of elliptic curves

34224 = 2⁴ · 3 · 23 · 31

Class	r	Atkin-Lehner	Eigenvalues
34224a (2 curves)	1	2+ 3+ 23+ 31+	2+ 3+  0 -4  0  6  2  0
Curve Equation t Generators 34224a1 [0,-1,0,-1826463,950682546] 2 [20895291583710:-269090675747072:20012875875] 34224a2 [0,-1,0,-1765628,1016895360] 2 [9985740:496999936:3375]
34224b (2 curves)	1	2+ 3+ 23+ 31+	2+ 3+  4  0 -2  2  2 -6
Curve Equation t Generators 34224b1 [0,-1,0,5424,-66672] 2 [62:710:1] 34224b2 [0,-1,0,-23736,-533232] 2 [552:12420:1]
34224c (1 curve)	2	2+ 3+ 23+ 31-	2+ 3+ -3 -3 -4 -4  2  5
Curve Equation t Generators 34224c1 [0,-1,0,28,39] 1 [-1:3:1]&[7:23:1]
34224d (2 curves)	0	2+ 3+ 23+ 31-	2+ 3+ -4  0  4 -2 -6  8
Curve Equation t 34224d1 [0,-1,0,2940,-36864] 2 34224d2 [0,-1,0,-13800,-304704] 2
34224e (1 curve)	1	2+ 3+ 23- 31-	2+ 3+  1  1  0  4 -2  1
Curve Equation t Generators 34224e1 [0,-1,0,-6640,210499] 1 [55:93:1]
34224f (1 curve)	1	2+ 3+ 23- 31-	2+ 3+ -1 -3  1 -2 -6 -4
Curve Equation t Generators 34224f1 [0,-1,0,-1296,17712] 1 [14:46:1]
34224g (1 curve)	1	2+ 3+ 23- 31-	2+ 3+  3 -1 -3  2  6 -4
Curve Equation t Generators 34224g1 [0,-1,0,-15224,-373728] 1 [-26:62:1]
34224h (1 curve)	1	2+ 3+ 23- 31-	2+ 3+ -3 -4  3  5 -3  5
Curve Equation t Generators 34224h1 [0,-1,0,88,336] 1 [10:46:1]
34224i (1 curve)	0	2+ 3- 23+ 31+	2+ 3-  3  2 -3 -1 -7 -3
Curve Equation t 34224i1 [0,1,0,-23064,-3387276] 1
34224j (1 curve)	0	2+ 3- 23+ 31+	2+ 3-  3 -3  3  6  6  4
Curve Equation t 34224j1 [0,1,0,-64,164] 1
34224k (4 curves)	1	2+ 3- 23+ 31-	2+ 3-  2  0 -4  6 -6  4
Curve Equation t Generators 34224k1 [0,1,0,-207,528] 2 [594960:7895888:3375] 34224k2 [0,1,0,-2852,57660] 4 [706:18720:1] 34224k3 [0,1,0,-2392,77348] 4 [-58:156:1] 34224k4 [0,1,0,-45632,3736740] 2 [367176:9445605:512]
34224l (2 curves)	1	2+ 3- 23+ 31-	2+ 3-  2  2 -4 -2 -8  2
Curve Equation t Generators 34224l1 [0,1,0,28,348] 2 [19:90:1] 34224l2 [0,1,0,-592,5060] 2 [8:30:1]
34224m (2 curves)	1	2+ 3- 23- 31+	2+ 3-  0 -4  0 -2 -2  0
Curve Equation t Generators 34224m1 [0,1,0,-23,0] 2 [192:424:27] 34224m2 [0,1,0,92,92] 2 [26:144:1]
34224n (2 curves)	0	2+ 3- 23- 31-	2+ 3-  2  2  6  6  0  0
Curve Equation t 34224n1 [0,1,0,-3632,-498012] 2 34224n2 [0,1,0,-118952,-15766380] 2
34224o (1 curve)	2	2- 3+ 23+ 31+	2- 3+  1 -1 -4 -4 -6  3
Curve Equation t Generators 34224o1 [0,-1,0,-430,-6761] 1 [41:207:1]&[385:7533:1]
34224p (1 curve)	0	2- 3+ 23+ 31+	2- 3+ -1  0  3 -5  1  1
Curve Equation t 34224p1 [0,-1,0,-2235136,1761820672] 1
34224q (1 curve)	0	2- 3+ 23+ 31+	2- 3+ -1  3 -3 -2 -2  4
Curve Equation t 34224q1 [0,-1,0,-5376,-147456] 1
34224r (2 curves)	2	2- 3+ 23+ 31+	2- 3+ -2 -4  2  2 -6 -6
Curve Equation t Generators 34224r1 [0,-1,0,-984,12528] 2 [-4:128:1]&[12:48:1] 34224r2 [0,-1,0,-15864,774384] 2 [-134:690:1]&[50:322:1]
34224s (2 curves)	0	2- 3+ 23+ 31+	2- 3+  3  1 -3  2 -6  4
Curve Equation t 34224s1 [0,-1,0,-86083944,-307390754448] 1 34224s2 [0,-1,0,-92393304,-259726172688] 1
34224t (2 curves)	0	2- 3+ 23+ 31+	2- 3+  4 -4  2  2  6 -6
Curve Equation t 34224t1 [0,-1,0,-3531576,-2571291792] 2 34224t2 [0,-1,0,-56615736,-163947138192] 2
34224u (1 curve)	1	2- 3+ 23+ 31-	2- 3+  1 -1  3 -2 -2  4
Curve Equation t Generators 34224u1 [0,-1,0,-760,-2192] 1 [-6:46:1]
34224v (1 curve)	1	2- 3+ 23+ 31-	2- 3+  1  4 -1  1 -3 -3
Curve Equation t Generators 34224v1 [0,-1,0,-5240,-145296] 1 [396:7728:1]
34224w (2 curves)	1	2- 3+ 23+ 31-	2- 3+ -2  2  0 -2  4 -2
Curve Equation t Generators 34224w1 [0,-1,0,-1282904,-5052248592] 2 [13717693094186:-587917041967458:4750104241] 34224w2 [0,-1,0,-52708184,-146410058256] 2 [-18345353978900644949945342770:-116981674241242877091203280718:4280674726248645280535279]
34224x (2 curves)	1	2- 3+ 23+ 31-	2- 3+ -2 -2 -4 -2  0  6
Curve Equation t Generators 34224x1 [0,-1,0,-95224,11345008] 2 [156:512:1] 34224x2 [0,-1,0,-1523704,724442224] 2 [690:1058:1]
34224y (2 curves)	1	2- 3+ 23- 31+	2- 3+ -2 -2  0 -2 -4 -6
Curve Equation t Generators 34224y1 [0,-1,0,456,-1872] 2 [12:72:1] 34224y2 [0,-1,0,-2024,-13776] 2 [-30:138:1]
34224z (2 curves)	1	2- 3+ 23- 31+	2- 3+  3  4 -6 -4  0  4
Curve Equation t Generators 34224z1 [0,-1,0,211,-2703] 1 [169:2198:1] 34224z2 [0,-1,0,-1949,83697] 1 [-11:322:1]
34224ba (1 curve)	0	2- 3+ 23- 31-	2- 3+  1  0 -2  4 -4 -8
Curve Equation t 34224ba1 [0,-1,0,-5,429] 1
34224bb (6 curves)	0	2- 3+ 23- 31-	2- 3+ -2  0  4 -2  2  4
Curve Equation t 34224bb1 [0,-1,0,-173264,-27701760] 2 34224bb2 [0,-1,0,-173344,-27674816] 4 34224bb3 [0,-1,0,-116304,-46247040] 2 34224bb4 [0,-1,0,-231664,-7379456] 8 34224bb5 [0,-1,0,910976,-59483840] 4 34224bb6 [0,-1,0,-2307424,1342694848] 4
34224bc (1 curve)	0	2- 3+ 23- 31-	2- 3+  3 -4  2  0  4  4
Curve Equation t 34224bc1 [0,-1,0,-41509,3269197] 1
34224bd (1 curve)	1	2- 3- 23+ 31+	2- 3-  3  5 -5  0 -2 -8
Curve Equation t Generators 34224bd1 [0,1,0,-44,24] 1 [-5:12:1]
34224be (2 curves)	1	2- 3- 23+ 31+	2- 3- -4  4 -6 -6 -2  2
Curve Equation t Generators 34224be1 [0,1,0,-581480,8843881524] 2 [910:-95232:1] 34224be2 [0,1,0,-67766120,212144602164] 2 [-7844:511014:1]
34224bf (1 curve)	0	2- 3- 23+ 31-	2- 3-  1  1  1 -6  6  4
Curve Equation t 34224bf1 [0,1,0,-240,1236] 1
34224bg (1 curve)	0	2- 3- 23+ 31-	2- 3-  1  1 -2  0  0  1
Curve Equation t 34224bg1 [0,1,0,-1710,-28269] 1
34224bh (4 curves)	0	2- 3- 23+ 31-	2- 3- -2  4 -4 -2 -2 -8
Curve Equation t 34224bh1 [0,1,0,-3504,47700] 2 34224bh2 [0,1,0,-23984,-1402284] 4 34224bh3 [0,1,0,5456,-4593580] 4 34224bh4 [0,1,0,-381104,-90682284] 2
34224bi (1 curve)	0	2- 3- 23- 31+	2- 3-  1 -1 -3  4 -6  0
Curve Equation t 34224bi1 [0,1,0,-15060,-716328] 1
34224bj (2 curves)	0	2- 3- 23- 31+	2- 3-  2 -2  0  6  4  2
Curve Equation t 34224bj1 [0,1,0,-19752,-1861452] 2 34224bj2 [0,1,0,-376872,-89141580] 2
34224bk (2 curves)	0	2- 3- 23- 31+	2- 3- -2  2  0 -2  0  6
Curve Equation t 34224bk1 [0,1,0,-205915384,1137247915220] 2 34224bk2 [0,1,0,-3294646264,72787155884756] 2
34224bl (1 curve)	0	2- 3- 23- 31+	2- 3-  3  2  5  3  5  1
Curve Equation t 34224bl1 [0,1,0,-87704,-19803756] 1
34224bm (2 curves)	1	2- 3- 23- 31-	2- 3-  0  0  0  6 -2  4
Curve Equation t Generators 34224bm1 [0,1,0,-488,4212] 2 [-2:72:1] 34224bm2 [0,1,0,-7928,269076] 2 [60:114:1]
34224bn (1 curve)	1	2- 3- 23- 31-	2- 3- -1  3  3 -2  2 -4
Curve Equation t Generators 34224bn1 [0,1,0,-494816,133738356] 1 [388:558:1]
34224bo (1 curve)	1	2- 3- 23- 31-	2- 3-  3 -3  3 -6 -2  4
Curve Equation t Generators 34224bo1 [0,1,0,-44184,-2954412] 1 [-84:414:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

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