Cremona's table of elliptic curves

4800 = 2⁶ · 3 · 5²

Class	r	Atkin-Lehner	Eigenvalues
4800a (4 curves)	1	2+ 3+ 5+	2+ 3+ 5+  0  0  2 -6  4
Curve Equation t Generators 4800a1 [0,-1,0,92,-938] 2 [218:1161:8] 4800a2 [0,-1,0,-1033,-11063] 4 [-17:36:1] 4800a3 [0,-1,0,-16033,-776063] 2 [152:525:1] 4800a4 [0,-1,0,-4033,87937] 2 [57:200:1]
4800b (8 curves)	1	2+ 3+ 5+	2+ 3+ 5+  0  4 -2 -2 -4
Curve Equation t Generators 4800b1 [0,-1,0,-33,11937] 2 [-13:100:1] 4800b2 [0,-1,0,-8033,275937] 4 [-7:576:1] 4800b3 [0,-1,0,-16033,-356063] 4 [-32:351:1] 4800b4 [0,-1,0,-128033,17675937] 2 [297:2400:1] 4800b5 [0,-1,0,-216033,-38556063] 4 [43329:1652300:27] 4800b6 [0,-1,0,55967,-2732063] 2 [57:800:1] 4800b7 [0,-1,0,-3456033,-2471796063] 2 [1778952639:21247565300:804357] 4800b8 [0,-1,0,-176033,-53316063] 2 [74494917536:-2285626983723:65450827]
4800c (6 curves)	1	2+ 3+ 5+	2+ 3+ 5+  0 -4 -2 -2  4
Curve Equation t Generators 4800c1 [0,-1,0,67,237] 2 [13:56:1] 4800c2 [0,-1,0,-433,2737] 4 [-8:75:1] 4800c3 [0,-1,0,-2433,-43263] 4 [-24:27:1] 4800c4 [0,-1,0,-6433,200737] 2 [51:52:1] 4800c5 [0,-1,0,-38433,-2887263] 2 [787:21300:1] 4800c6 [0,-1,0,1567,-175263] 2 [776:21627:1]
4800d (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+  1 -4 -3  4 -1
Curve Equation t Generators 4800d1 [0,-1,0,417,-5463] 1 [128:1459:1]
4800e (2 curves)	1	2+ 3+ 5+	2+ 3+ 5+  3 -2  1 -2  5
Curve Equation t Generators 4800e1 [0,-1,0,7,27] 1 [-2:1:1] 4800e2 [0,-1,0,-833,-9213] 1 [13258:41791:343]
4800f (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+ -3  0  5  0 -5
Curve Equation t Generators 4800f1 [0,-1,0,-183,1017] 1 [8:1:1]
4800g (4 curves)	1	2+ 3+ 5+	2+ 3+ 5+  4 -4  6 -2 -4
Curve Equation t Generators 4800g1 [0,-1,0,-22508,1307262] 2 [283:4186:1] 4800g2 [0,-1,0,-22633,1292137] 4 [-119:1512:1] 4800g3 [0,-1,0,-49633,-2352863] 2 [-144:1337:1] 4800g4 [0,-1,0,2367,3967137] 2 [1072:35175:1]
4800h (4 curves)	1	2+ 3+ 5+	2+ 3+ 5+ -4  4 -2  6 -4
Curve Equation t Generators 4800h1 [0,-1,0,-108,462] 2 [11:22:1] 4800h2 [0,-1,0,-233,-663] 4 [-8:25:1] 4800h3 [0,-1,0,-3233,-69663] 2 [-32:1:1] 4800h4 [0,-1,0,767,-5663] 2 [32:225:1]
4800i (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  1  4  3 -4  1
Curve Equation t 4800i1 [0,-1,0,17,37] 1
4800j (2 curves)	0	2+ 3+ 5-	2+ 3+ 5- -1 -6 -5 -6 -5
Curve Equation t 4800j1 [0,-1,0,-1333,-26963] 1 4800j2 [0,-1,0,-121333,-16226963] 1
4800k (2 curves)	0	2+ 3+ 5-	2+ 3+ 5- -2 -2 -2  6 -8
Curve Equation t 4800k1 [0,-1,0,3167,-58463] 2 4800k2 [0,-1,0,-16833,-518463] 2
4800l (4 curves)	0	2+ 3+ 5-	2+ 3+ 5- -2 -2  6 -2  0
Curve Equation t 4800l1 [0,-1,0,-193,-1343] 2 4800l2 [0,-1,0,-3393,-74943] 2 4800l3 [0,-1,0,-1793,141057] 2 4800l4 [0,-1,0,-52993,4697857] 2
4800m (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  3 -2  3  6  7
Curve Equation t 4800m1 [0,-1,0,667,-963] 1
4800n (1 curve)	0	2+ 3+ 5-	2+ 3+ 5- -3  0 -5  0  5
Curve Equation t 4800n1 [0,-1,0,-4583,-117963] 1
4800o (2 curves)	0	2+ 3+ 5-	2+ 3+ 5-  4  4  0  4  0
Curve Equation t 4800o1 [0,-1,0,-1333,18037] 2 4800o2 [0,-1,0,1167,75537] 2
4800p (1 curve)	0	2+ 3+ 5-	2+ 3+ 5- -5  6  3 -2 -1
Curve Equation t 4800p1 [0,-1,0,-933,13437] 1
4800q (4 curves)	0	2+ 3- 5+	2+ 3- 5+  0  0  2 -6 -4
Curve Equation t 4800q1 [0,1,0,92,938] 2 4800q2 [0,1,0,-1033,11063] 4 4800q3 [0,1,0,-4033,-87937] 2 4800q4 [0,1,0,-16033,776063] 2
4800r (6 curves)	0	2+ 3- 5+	2+ 3- 5+  0  4  6  6  4
Curve Equation t 4800r1 [0,1,0,-1533,22563] 2 4800r2 [0,1,0,-2033,6063] 4 4800r3 [0,1,0,-20033,-1091937] 4 4800r4 [0,1,0,7967,56063] 2 4800r5 [0,1,0,-320033,-69791937] 2 4800r6 [0,1,0,-8033,-2375937] 2
4800s (2 curves)	0	2+ 3- 5+	2+ 3- 5+  1 -6  5  6 -5
Curve Equation t 4800s1 [0,1,0,-53,-237] 1 4800s2 [0,1,0,-4853,-131757] 1
4800t (1 curve)	0	2+ 3- 5+	2+ 3- 5+ -1  4 -3  4  1
Curve Equation t 4800t1 [0,1,0,417,5463] 1
4800u (1 curve)	0	2+ 3- 5+	2+ 3- 5+  3  0  5  0  5
Curve Equation t 4800u1 [0,1,0,-183,-1017] 1
4800v (1 curve)	0	2+ 3- 5+	2+ 3- 5+ -3 -2 -3 -6  7
Curve Equation t 4800v1 [0,1,0,27,3] 1
4800w (8 curves)	0	2+ 3- 5+	2+ 3- 5+  4  0  2 -6  4
Curve Equation t 4800w1 [0,1,0,2367,136863] 2 4800w2 [0,1,0,-29633,1768863] 4 4800w3 [0,1,0,-21633,-4015137] 2 4800w4 [0,1,0,-109633,-12071137] 2 4800w5 [0,1,0,-461633,120568863] 2 4800w6 [0,1,0,-533633,-149935137] 4 4800w7 [0,1,0,-8533633,-9597935137] 2 4800w8 [0,1,0,-725633,-32623137] 2
4800x (4 curves)	0	2+ 3- 5+	2+ 3- 5+  4 -4 -2  6  4
Curve Equation t 4800x1 [0,1,0,-108,-462] 2 4800x2 [0,1,0,-233,663] 4 4800x3 [0,1,0,-3233,69663] 2 4800x4 [0,1,0,767,5663] 2
4800y (4 curves)	0	2+ 3- 5+	2+ 3- 5+ -4  0 -6  2 -4
Curve Equation t 4800y1 [0,1,0,367,-1137] 2 4800y2 [0,1,0,-1633,-11137] 4 4800y3 [0,1,0,-21633,-1231137] 2 4800y4 [0,1,0,-13633,600863] 2
4800z (4 curves)	0	2+ 3- 5+	2+ 3- 5+ -4  4  6 -2  4
Curve Equation t 4800z1 [0,1,0,-22508,-1307262] 2 4800z2 [0,1,0,-22633,-1292137] 4 4800z3 [0,1,0,-49633,2352863] 2 4800z4 [0,1,0,2367,-3967137] 2
4800ba (1 curve)	0	2+ 3- 5+	2+ 3- 5+  5  6 -3  2 -1
Curve Equation t 4800ba1 [0,1,0,-23333,1632963] 1
4800bb (1 curve)	1	2+ 3- 5-	2+ 3- 5- -1 -4  3 -4 -1
Curve Equation t Generators 4800bb1 [0,1,0,17,-37] 1 [2:3:1]
4800bc (2 curves)	1	2+ 3- 5-	2+ 3- 5-  2 -2  2 -6 -8
Curve Equation t Generators 4800bc1 [0,1,0,127,-417] 2 [13:60:1] 4800bc2 [0,1,0,-673,-4417] 2 [-13:48:1]
4800bd (4 curves)	1	2+ 3- 5-	2+ 3- 5-  2 -2 -6  2  0
Curve Equation t Generators 4800bd1 [0,1,0,-4833,-177537] 2 [913601:18367500:2197] 4800bd2 [0,1,0,-84833,-9537537] 2 [14241:260000:27] 4800bd3 [0,1,0,-44833,17542463] 2 [-67:4500:1] 4800bd4 [0,1,0,-1324833,584582463] 2 [579:3456:1]
4800be (1 curve)	1	2+ 3- 5-	2+ 3- 5-  3  0 -5  0 -5
Curve Equation t Generators 4800be1 [0,1,0,-4583,117963] 1 [58:225:1]
4800bf (2 curves)	1	2+ 3- 5-	2+ 3- 5- -3 -2 -1  2  5
Curve Equation t Generators 4800bf1 [0,1,0,-33,-87] 1 [8:15:1] 4800bf2 [0,1,0,167,3713] 1 [8:75:1]
4800bg (2 curves)	1	2+ 3- 5-	2+ 3- 5- -4  4  0 -4  0
Curve Equation t Generators 4800bg1 [0,1,0,-53,123] 2 [-2:15:1] 4800bg2 [0,1,0,47,623] 2 [-1:24:1]
4800bh (4 curves)	0	2- 3+ 5+	2- 3+ 5+  0  4  2  2  8
Curve Equation t 4800bh1 [0,-1,0,-508,-4238] 2 4800bh2 [0,-1,0,-633,-1863] 4 4800bh3 [0,-1,0,-5633,163137] 2 4800bh4 [0,-1,0,2367,-16863] 2
4800bi (6 curves)	0	2- 3+ 5+	2- 3+ 5+  0 -4  6  6 -4
Curve Equation t 4800bi1 [0,-1,0,-1533,-22563] 2 4800bi2 [0,-1,0,-2033,-6063] 4 4800bi3 [0,-1,0,-20033,1091937] 4 4800bi4 [0,-1,0,7967,-56063] 2 4800bi5 [0,-1,0,-320033,69791937] 2 4800bi6 [0,-1,0,-8033,2375937] 2
4800bj (1 curve)	0	2- 3+ 5+	2- 3+ 5+  1  0  1  0  3
Curve Equation t 4800bj1 [0,-1,0,-3,-3] 1
4800bk (2 curves)	0	2- 3+ 5+	2- 3+ 5+ -1  6  5  6  5
Curve Equation t 4800bk1 [0,-1,0,-53,237] 1 4800bk2 [0,-1,0,-4853,131757] 1
4800bl (1 curve)	0	2- 3+ 5+	2- 3+ 5+  3  2 -3 -6 -7
Curve Equation t 4800bl1 [0,-1,0,27,-3] 1
4800bm (1 curve)	0	2- 3+ 5+	2- 3+ 5+ -3  4 -7 -4 -1
Curve Equation t 4800bm1 [0,-1,0,-43,-803] 1
4800bn (4 curves)	0	2- 3+ 5+	2- 3+ 5+  4  0 -2  6  0
Curve Equation t 4800bn1 [0,-1,0,92,3562] 2 4800bn2 [0,-1,0,-3033,62937] 4 4800bn3 [0,-1,0,-8033,-192063] 2 4800bn4 [0,-1,0,-48033,4067937] 4
4800bo (4 curves)	0	2- 3+ 5+	2- 3+ 5+  4  0 -6  2  4
Curve Equation t 4800bo1 [0,-1,0,367,1137] 2 4800bo2 [0,-1,0,-1633,11137] 4 4800bo3 [0,-1,0,-13633,-600863] 2 4800bo4 [0,-1,0,-21633,1231137] 2
4800bp (8 curves)	0	2- 3+ 5+	2- 3+ 5+ -4  0  2 -6 -4
Curve Equation t 4800bp1 [0,-1,0,2367,-136863] 2 4800bp2 [0,-1,0,-29633,-1768863] 4 4800bp3 [0,-1,0,-21633,4015137] 2 4800bp4 [0,-1,0,-461633,-120568863] 2 4800bp5 [0,-1,0,-109633,12071137] 2 4800bp6 [0,-1,0,-533633,149935137] 4 4800bp7 [0,-1,0,-725633,32623137] 2 4800bp8 [0,-1,0,-8533633,9597935137] 2
4800bq (1 curve)	0	2- 3+ 5+	2- 3+ 5+ -5 -6 -3  2  1
Curve Equation t 4800bq1 [0,-1,0,-23333,-1632963] 1
4800br (1 curve)	1	2- 3+ 5-	2- 3+ 5-  1  0 -1  0 -3
Curve Equation t Generators 4800br1 [0,-1,0,-83,537] 1 [-8:25:1]
4800bs (2 curves)	1	2- 3+ 5-	2- 3+ 5-  2  6  2 -6 -4
Curve Equation t Generators 4800bs1 [0,-1,0,167,-7463] 2 [53:384:1] 4800bs2 [0,-1,0,-4833,-122463] 2 [-39:72:1]
4800bt (2 curves)	1	2- 3+ 5-	2- 3+ 5-  2 -6 -2  6  4
Curve Equation t Generators 4800bt1 [0,-1,0,7,57] 2 [1:8:1] 4800bt2 [0,-1,0,-193,1057] 2 [-3:40:1]
4800bu (2 curves)	1	2- 3+ 5-	2- 3+ 5- -2  2  2 -6  8
Curve Equation t Generators 4800bu1 [0,-1,0,127,417] 2 [7:40:1] 4800bu2 [0,-1,0,-673,4417] 2 [-3:80:1]
4800bv (4 curves)	1	2- 3+ 5-	2- 3+ 5- -2  2 -6  2  0
Curve Equation t Generators 4800bv1 [0,-1,0,-4833,177537] 2 [-19:512:1] 4800bv2 [0,-1,0,-84833,9537537] 2 [-83:4000:1] 4800bv3 [0,-1,0,-44833,-17542463] 2 [19356711:2333974528:1331] 4800bv4 [0,-1,0,-1324833,-584582463] 2 [58173:14027904:1]
4800bw (2 curves)	1	2- 3+ 5-	2- 3+ 5-  3  2 -1  2 -5
Curve Equation t Generators 4800bw1 [0,-1,0,-33,87] 1 [2:5:1] 4800bw2 [0,-1,0,167,-3713] 1 [42:275:1]
4800bx (1 curve)	1	2- 3+ 5-	2- 3+ 5- -3 -4  7  4  1
Curve Equation t Generators 4800bx1 [0,-1,0,-1083,102537] 1 [56:463:1]
4800by (2 curves)	1	2- 3+ 5-	2- 3+ 5-  4 -4  0 -4  0
Curve Equation t Generators 4800by1 [0,-1,0,-53,-123] 2 [-4:3:1] 4800by2 [0,-1,0,47,-623] 2 [16:63:1]
4800bz (2 curves)	1	2- 3+ 5-	2- 3+ 5- -4  0  4  0 -8
Curve Equation t Generators 4800bz1 [0,-1,0,-3208,-81338] 2 [748210:20391669:1000] 4800bz2 [0,-1,0,-53833,-4789463] 2 [2992:163125:1]
4800ca (2 curves)	1	2- 3+ 5-	2- 3+ 5- -4  0 -4  0  8
Curve Equation t Generators 4800ca1 [0,-1,0,-128,702] 2 [7:10:1] 4800ca2 [0,-1,0,-2153,39177] 2 [23:36:1]
4800cb (6 curves)	1	2- 3- 5+	2- 3- 5+  0  4 -2 -2 -4
Curve Equation t Generators 4800cb1 [0,1,0,67,-237] 2 [273:1072:27] 4800cb2 [0,1,0,-433,-2737] 4 [47:288:1] 4800cb3 [0,1,0,-6433,-200737] 2 [97:312:1] 4800cb4 [0,1,0,-2433,43263] 4 [-27:300:1] 4800cb5 [0,1,0,-38433,2887263] 2 [114:21:1] 4800cb6 [0,1,0,1567,175263] 2 [7:432:1]
4800cc (4 curves)	1	2- 3- 5+	2- 3- 5+  0 -4  2  2 -8
Curve Equation t Generators 4800cc1 [0,1,0,-508,4238] 2 [554:4425:8] 4800cc2 [0,1,0,-633,1863] 4 [-22:75:1] 4800cc3 [0,1,0,-5633,-163137] 2 [-41:24:1] 4800cc4 [0,1,0,2367,16863] 2 [2:147:1]
4800cd (8 curves)	1	2- 3- 5+	2- 3- 5+  0 -4 -2 -2  4
Curve Equation t Generators 4800cd1 [0,1,0,-33,-11937] 2 [113:1200:1] 4800cd2 [0,1,0,-8033,-275937] 4 [967:29952:1] 4800cd3 [0,1,0,-128033,-17675937] 2 [26859:782704:27] 4800cd4 [0,1,0,-16033,356063] 4 [-127:600:1] 4800cd5 [0,1,0,-216033,38556063] 4 [138:3375:1] 4800cd6 [0,1,0,55967,2732063] 2 [-31:984:1] 4800cd7 [0,1,0,-3456033,2471796063] 2 [1077:228:1] 4800cd8 [0,1,0,-176033,53316063] 2 [-41:7776:1]
4800ce (1 curve)	1	2- 3- 5+	2- 3- 5+ -1  0  1  0 -3
Curve Equation t Generators 4800ce1 [0,1,0,-3,3] 1 [2:3:1]
4800cf (1 curve)	1	2- 3- 5+	2- 3- 5+  3 -4 -7 -4  1
Curve Equation t Generators 4800cf1 [0,1,0,-43,803] 1 [2:27:1]
4800cg (2 curves)	1	2- 3- 5+	2- 3- 5+ -3  2  1 -2 -5
Curve Equation t Generators 4800cg1 [0,1,0,7,-27] 1 [4:9:1] 4800cg2 [0,1,0,-833,9213] 1 [12:33:1]
4800ch (4 curves)	1	2- 3- 5+	2- 3- 5+ -4  0 -2  6  0
Curve Equation t Generators 4800ch1 [0,1,0,92,-3562] 2 [29:156:1] 4800ch2 [0,1,0,-3033,-62937] 4 [-33:48:1] 4800ch3 [0,1,0,-48033,-4067937] 2 [273:1800:1] 4800ch4 [0,1,0,-8033,192063] 4 [-77:600:1]
4800ci (2 curves)	0	2- 3- 5-	2- 3- 5-  1  6 -5 -6  5
Curve Equation t 4800ci1 [0,1,0,-1333,26963] 1 4800ci2 [0,1,0,-121333,16226963] 1
4800cj (1 curve)	0	2- 3- 5-	2- 3- 5- -1  0 -1  0  3
Curve Equation t 4800cj1 [0,1,0,-83,-537] 1
4800ck (2 curves)	0	2- 3- 5-	2- 3- 5-  2  2 -2  6  8
Curve Equation t 4800ck1 [0,1,0,3167,58463] 2 4800ck2 [0,1,0,-16833,518463] 2
4800cl (4 curves)	0	2- 3- 5-	2- 3- 5-  2  2  6 -2  0
Curve Equation t 4800cl1 [0,1,0,-193,1343] 2 4800cl2 [0,1,0,-3393,74943] 2 4800cl3 [0,1,0,-1793,-141057] 2 4800cl4 [0,1,0,-52993,-4697857] 2
4800cm (2 curves)	0	2- 3- 5-	2- 3- 5- -2  6 -2  6 -4
Curve Equation t 4800cm1 [0,1,0,7,-57] 2 4800cm2 [0,1,0,-193,-1057] 2
4800cn (2 curves)	0	2- 3- 5-	2- 3- 5- -2 -6  2 -6  4
Curve Equation t 4800cn1 [0,1,0,167,7463] 2 4800cn2 [0,1,0,-4833,122463] 2
4800co (1 curve)	0	2- 3- 5-	2- 3- 5-  3  4  7  4 -1
Curve Equation t 4800co1 [0,1,0,-1083,-102537] 1
4800cp (1 curve)	0	2- 3- 5-	2- 3- 5- -3  2  3  6 -7
Curve Equation t 4800cp1 [0,1,0,667,963] 1
4800cq (2 curves)	0	2- 3- 5-	2- 3- 5-  4  0  4  0  8
Curve Equation t 4800cq1 [0,1,0,-3208,81338] 2 4800cq2 [0,1,0,-53833,4789463] 2
4800cr (2 curves)	0	2- 3- 5-	2- 3- 5-  4  0 -4  0 -8
Curve Equation t 4800cr1 [0,1,0,-128,-702] 2 4800cr2 [0,1,0,-2153,-39177] 2
4800cs (2 curves)	0	2- 3- 5-	2- 3- 5- -4 -4  0  4  0
Curve Equation t 4800cs1 [0,1,0,-1333,-18037] 2 4800cs2 [0,1,0,1167,-75537] 2
4800ct (1 curve)	0	2- 3- 5-	2- 3- 5-  5 -6  3 -2  1
Curve Equation t 4800ct1 [0,1,0,-933,-13437] 1

Data from Elliptic Curve Data by J. E. Cremona.
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Part of Computational Number Theory
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