Cremona's table of elliptic curves

67600 = 2⁴ · 5² · 13²

Class	r	Atkin-Lehner	Eigenvalues
67600a (4 curves)	1	2+ 5+ 13+	2+  0 5+  0 -4 13+  6  4
Curve Equation t Generators 67600a1 [0,0,0,-97175,-11534250] 2 [-1254741:2381016:6859] 67600a2 [0,0,0,-181675,11534250] 4 [29:2508:1] 67600a3 [0,0,0,663325,88429250] 2 [127533:-8897966:27] 67600a4 [0,0,0,-2378675,1411023250] 2 [285:27500:1]
67600b (4 curves)	1	2+ 5+ 13+	2+  0 5+  4  4 13+ -2  4
Curve Equation t Generators 67600b1 [0,0,0,-8450,-274625] 2 [-1759240905:-3842382376:41063625] 67600b2 [0,0,0,-29575,1647750] 4 [-7555:224112:125] 67600b3 [0,0,0,54925,9337250] 2 [5330:147875:8] 67600b4 [0,0,0,-452075,116990250] 2 [-235:14500:1]
67600c (1 curve)	1	2+ 5+ 13+	2+  1 5+  1  1 13+ -3  7
Curve Equation t Generators 67600c1 [0,1,0,-108,-337] 1 [13:25:1]
67600d (1 curve)	1	2+ 5+ 13+	2+  1 5+ -1 -1 13+ -3 -7
Curve Equation t Generators 67600d1 [0,1,0,-18308,-667237] 1 [-566:4225:8]
67600e (1 curve)	1	2+ 5+ 13+	2+  1 5+ -5 -2 13+  3 -2
Curve Equation t Generators 67600e1 [0,1,0,-69008,7279988] 1 [134:-676:1]
67600f (1 curve)	1	2+ 5+ 13+	2+ -1 5+  0 -2 13+  2  8
Curve Equation t Generators 67600f1 [0,-1,0,-140833,-7072963] 1 [-2309716:9827857:6859]
67600g (1 curve)	1	2+ 5+ 13+	2+ -1 5+  3  1 13+ -1 -1
Curve Equation t Generators 67600g1 [0,-1,0,-10508,-411113] 1 [-12738:125:216]
67600h (1 curve)	1	2+ 5+ 13+	2+ -1 5+  3 -3 13+  3 -5
Curve Equation t Generators 67600h1 [0,-1,0,-238008,-1639613] 1 [-534:29875:8]
67600i (1 curve)	1	2+ 5+ 13+	2+ -1 5+  3  5 13+ -5 -1
Curve Equation t Generators 67600i1 [0,-1,0,-1408,-19813] 1 [47:125:1]
67600j (1 curve)	1	2+ 5+ 13+	2+ -1 5+ -3 -1 13+ -1  1
Curve Equation t Generators 67600j1 [0,-1,0,-1775908,-910318813] 1 [-263459:22625:343]
67600k (1 curve)	1	2+ 5+ 13+	2+ -1 5+ -3  3 13+  3  5
Curve Equation t Generators 67600k1 [0,-1,0,-1408,-313] 1 [-13:125:1]
67600l (1 curve)	1	2+ 5+ 13+	2+ -1 5+ -3 -5 13+ -5  1
Curve Equation t Generators 67600l1 [0,-1,0,-238008,-44481113] 1 [-293:125:1]
67600m (2 curves)	1	2+ 5+ 13+	2+  2 5+  0  2 13+ -2  2
Curve Equation t Generators 67600m1 [0,-1,0,-85908,9569312] 2 [-8376:67600:27] 67600m2 [0,-1,0,-1408,27483312] 2 [9057:861900:1]
67600n (1 curve)	1	2+ 5+ 13+	2+  2 5+  3  1 13+  5 -4
Curve Equation t Generators 67600n1 [0,-1,0,45912,9569312] 1 [-26799806:237684642:205379]
67600o (1 curve)	1	2+ 5+ 13+	2+  2 5+  3  5 13+  2 -5
Curve Equation t Generators 67600o1 [0,-1,0,-1408,105312] 1 [12:300:1]
67600p (1 curve)	1	2+ 5+ 13+	2+  2 5+ -3  3 13+ -3  4
Curve Equation t Generators 67600p1 [0,-1,0,-1408,64752] 1 [438:9126:1]
67600q (1 curve)	1	2+ 5+ 13+	2+  2 5+ -3 -5 13+  2  5
Curve Equation t Generators 67600q1 [0,-1,0,-238008,230418512] 1 [-792766:36046050:2197]
67600r (1 curve)	1	2+ 5+ 13+	2+  3 5+ -2 -2 13+ -2  4
Curve Equation t Generators 67600r1 [0,0,0,-16900,-746980] 1 [-737256:709631:13824]
67600s (1 curve)	1	2+ 5+ 13+	2+ -3 5+ -2  1 13+ -5  1
Curve Equation t Generators 67600s1 [0,0,0,845,21970] 1 [39:338:1]
67600t (1 curve)	1	2+ 5+ 13+	2+ -3 5+  3 -5 13+ -3  5
Curve Equation t Generators 67600t1 [0,0,0,-4339075,-3452310875] 1 [-615160:2640625:512]
67600u (1 curve)	1	2+ 5+ 13+	2+ -3 5+ -3  5 13+ -3 -5
Curve Equation t Generators 67600u1 [0,0,0,-25675,-1571375] 1 [640:15625:1]
67600v (2 curves)	0	2+ 5- 13+	2+  0 5-  4 -2 13+  4 -2
Curve Equation t 67600v1 [0,0,0,-5915,109850] 2 67600v2 [0,0,0,-39715,-2965950] 2
67600w (2 curves)	2	2+ 5- 13+	2+  0 5- -4 -2 13+ -4 -2
Curve Equation t Generators 67600w1 [0,0,0,-147875,13731250] 2 [1950:-84500:1]&[-159:5764:1] 67600w2 [0,0,0,-992875,-370743750] 2 [-601:2982:1]&[2054:79092:1]
67600x (1 curve)	0	2+ 5- 13+	2+  1 5-  0 -2 13+ -2  8
Curve Equation t 67600x1 [0,1,0,-5633,-58837] 1
67600y (2 curves)	0	2+ 5- 13+	2+  2 5- -2 -4 13+  0 -4
Curve Equation t 67600y1 [0,-1,0,-563,2222] 2 67600y2 [0,-1,0,-4788,-124528] 2
67600z (2 curves)	0	2+ 5- 13+	2+ -2 5-  2 -4 13+  0 -4
Curve Equation t 67600z1 [0,1,0,-14083,249588] 2 67600z2 [0,1,0,-119708,-15805412] 2
67600ba (1 curve)	0	2+ 5- 13+	2+ -2 5-  3  3 13+  3  4
Curve Equation t 67600ba1 [0,1,0,-35208,8023588] 1
67600bb (1 curve)	0	2+ 5- 13+	2+ -2 5- -3  1 13+ -5 -4
Curve Equation t 67600bb1 [0,1,0,1147792,1198459588] 1
67600bc (1 curve)	0	2+ 5- 13+	2+  3 5-  2  1 13+  5  1
Curve Equation t 67600bc1 [0,0,0,21125,2746250] 1
67600bd (1 curve)	0	2+ 5- 13+	2+ -3 5-  2 -2 13+  2  4
Curve Equation t 67600bd1 [0,0,0,-422500,-93372500] 1
67600be (4 curves)	2	2- 5+ 13+	2-  0 5+  0  0 13+ -2 -8
Curve Equation t Generators 67600be1 [0,0,0,-452075,42292250] 2 [-65:8450:1]&[95:450:1] 67600be2 [0,0,0,-5860075,5455700250] 4 [341:59136:1]&[1205:12000:1] 67600be3 [0,0,0,-4508075,8039372250] 2 [2895:138750:1]&[3770:211250:1] 67600be4 [0,0,0,-93740075,349330140250] 4 [261:569984:1]&[1365:473200:1]
67600bf (2 curves)	0	2- 5+ 13+	2-  0 5+  2 -2 13+ -6 -6
Curve Equation t 67600bf1 [0,0,0,-16900,823875] 2 67600bf2 [0,0,0,4225,2746250] 2
67600bg (1 curve)	0	2- 5+ 13+	2-  0 5+  3  3 13+  1  4
Curve Equation t 67600bg1 [0,0,0,105625,13731250] 1
67600bh (2 curves)	0	2- 5+ 13+	2-  0 5+  3 -3 13+  4  7
Curve Equation t 67600bh1 [0,0,0,-59264075,-286174079750] 1 67600bh2 [0,0,0,-5200244075,156020753060250] 1
67600bi (2 curves)	0	2- 5+ 13+	2-  0 5+ -3  3 13+  4 -7
Curve Equation t 67600bi1 [0,0,0,-350675,-130256750] 1 67600bi2 [0,0,0,-30770675,71015363250] 1
67600bj (2 curves)	0	2- 5+ 13+	2-  0 5+  4 -4 13+ -3  0
Curve Equation t 67600bj1 [0,0,0,54925,-21420750] 1 67600bj2 [0,0,0,-26309075,51959599250] 1
67600bk (2 curves)	0	2- 5+ 13+	2-  0 5+ -4  4 13+ -3  0
Curve Equation t 67600bk1 [0,0,0,325,-9750] 1 67600bk2 [0,0,0,-155675,23650250] 1
67600bl (2 curves)	0	2- 5+ 13+	2-  1 5+  1  3 13+  3  5
Curve Equation t 67600bl1 [0,1,0,-758,-8137] 1 67600bl2 [0,1,0,-7258,232363] 1
67600bm (2 curves)	0	2- 5+ 13+	2-  1 5+  1  3 13+  3 -7
Curve Equation t 67600bm1 [0,1,0,-4522158,3527495063] 1 67600bm2 [0,1,0,-361534658,2645777007563] 1
67600bn (3 curves)	0	2- 5+ 13+	2-  1 5+  1  6 13+  3  2
Curve Equation t 67600bn1 [0,1,0,32392,-3671212] 1 67600bn2 [0,1,0,-305608,129500788] 1 67600bn3 [0,1,0,-31063608,66628296788] 1
67600bo (2 curves)	0	2- 5+ 13+	2-  1 5+ -1 -3 13+  3 -5
Curve Equation t 67600bo1 [0,1,0,-128158,-17364437] 1 67600bo2 [0,1,0,-1226658,515408063] 1
67600bp (2 curves)	0	2- 5+ 13+	2-  1 5+ -1 -3 13+  3  7
Curve Equation t 67600bp1 [0,1,0,-26758,1597363] 1 67600bp2 [0,1,0,-2139258,1203609863] 1
67600bq (2 curves)	0	2- 5+ 13+	2-  1 5+ -2  2 13+ -2  0
Curve Equation t 67600bq1 [0,1,0,-265893,-48669997] 1 67600bq2 [0,1,0,-34363333,77522302963] 1
67600br (4 curves)	0	2- 5+ 13+	2-  1 5+ -2 -3 13+  3  5
Curve Equation t 67600br1 [0,1,0,-8168,-345292] 1 67600br2 [0,1,0,59432,2547988] 1 67600br3 [0,1,0,-35208,29993588] 1 67600br4 [0,1,0,-8485208,9510893588] 1
67600bs (2 curves)	0	2- 5+ 13+	2-  1 5+  4 -6 13+ -6 -4
Curve Equation t 67600bs1 [0,1,0,-9013,-308957] 1 67600bs2 [0,1,0,-144213,20971523] 1
67600bt (1 curve)	2	2- 5+ 13+	2- -1 5+ -2 -2 13+ -2  0
Curve Equation t Generators 67600bt1 [0,-1,0,-2253,28417] 1 [13:34:1]&[61:-338:1]
67600bu (1 curve)	0	2- 5+ 13+	2- -1 5+  4  1 13+  7 -3
Curve Equation t 67600bu1 [0,-1,0,809792,-3096921088] 1
67600bv (1 curve)	0	2- 5+ 13+	2- -1 5+  5  5 13+  1  3
Curve Equation t 67600bv1 [0,-1,0,-128158,-4056313] 1
67600bw (1 curve)	2	2- 5+ 13+	2- -1 5+ -5 -5 13+  1 -3
Curve Equation t Generators 67600bw1 [0,-1,0,-758,-1613] 1 [-3:25:1]&[77:625:1]
67600bx (2 curves)	0	2- 5+ 13+	2-  2 5+ -2  4 13+ -2  0
Curve Equation t 67600bx1 [0,-1,0,-1188633,-498393988] 2 67600bx2 [0,-1,0,-1167508,-516983988] 2
67600by (2 curves)	0	2- 5+ 13+	2-  2 5+  4 -2 13+ -2  6
Curve Equation t 67600by1 [0,-1,0,-56853008,164994264512] 2 67600by2 [0,-1,0,-51445008,197636952512] 2
67600bz (2 curves)	0	2- 5+ 13+	2- -2 5+  1  3 13+ -3 -4
Curve Equation t 67600bz1 [0,1,0,-1725208,-885986412] 1 67600bz2 [0,1,0,6724792,-4215286412] 1
67600ca (2 curves)	0	2- 5+ 13+	2- -2 5+  1  3 13+  6  5
Curve Equation t 67600ca1 [0,1,0,-4008,-104012] 1 67600ca2 [0,1,0,21992,-156012] 1
67600cb (2 curves)	0	2- 5+ 13+	2- -2 5+ -1 -3 13+  6 -5
Curve Equation t 67600cb1 [0,1,0,-677408,-225804812] 1 67600cb2 [0,1,0,3716592,-357624812] 1
67600cc (4 curves)	0	2- 5+ 13+	2- -2 5+ -2  0 13+  6 -4
Curve Equation t 67600cc1 [0,1,0,-5633,-113762] 2 67600cc2 [0,1,0,15492,-747512] 2 67600cc3 [0,1,0,-174633,28024738] 2 67600cc4 [0,1,0,-153508,35080488] 2
67600cd (2 curves)	0	2- 5+ 13+	2- -2 5+  4  0 13+ -3  2
Curve Equation t 67600cd1 [0,1,0,-108,1288] 1 67600cd2 [0,1,0,-13108,573288] 1
67600ce (2 curves)	0	2- 5+ 13+	2- -2 5+  4  2 13+ -2 -6
Curve Equation t 67600ce1 [0,1,0,-69008,-1508012] 2 67600ce2 [0,1,0,268992,-11648012] 2
67600cf (4 curves)	0	2- 5+ 13+	2- -2 5+  4 -6 13+  6  2
Curve Equation t 67600cf1 [0,1,0,-2198408,-1247916812] 2 67600cf2 [0,1,0,-846408,-2764860812] 2 67600cf3 [0,1,0,-14028408,19407263188] 2 67600cf4 [0,1,0,7603592,73876639188] 2
67600cg (2 curves)	0	2- 5+ 13+	2- -2 5+ -4  0 13+ -3 -2
Curve Equation t 67600cg1 [0,1,0,-18308,2902888] 1 67600cg2 [0,1,0,-2215308,1268374888] 1
67600ch (2 curves)	0	2- 5+ 13+	2- -2 5+ -5 -3 13+ -3 -4
Curve Equation t 67600ch1 [0,1,0,-352928,101919988] 1 67600ch2 [0,1,0,-30637728,65262695668] 1
67600ci (1 curve)	0	2- 5+ 13+	2-  3 5+  0 -3 13+  7  1
Curve Equation t 67600ci1 [0,0,0,-59995,-5690230] 1
67600cj (1 curve)	0	2- 5+ 13+	2-  3 5+  1  5 13+ -3  3
Curve Equation t 67600cj1 [0,0,0,-4225,-105625] 1
67600ck (1 curve)	0	2- 5+ 13+	2-  3 5+ -1 -5 13+ -3 -3
Curve Equation t 67600ck1 [0,0,0,-714025,-232058125] 1
67600cl (2 curves)	0	2- 5+ 13+	2- -3 5+ -1 -2 13+  3  6
Curve Equation t 67600cl1 [0,0,0,-181675,-45587750] 1 67600cl2 [0,0,0,-14377675,23022912250] 1
67600cm (1 curve)	0	2- 5+ 13+	2- -3 5+  3 -3 13+  7 -1
Curve Equation t 67600cm1 [0,0,0,-54925,-3570125] 1
67600cn (1 curve)	2	2- 5+ 13+	2- -3 5+ -3  3 13+  7  1
Curve Equation t Generators 67600cn1 [0,0,0,-325,-1625] 1 [-10:25:1]&[30:125:1]
67600co (2 curves)	1	2- 5+ 13-	2-  1 5+  2  0 13-  2  4
Curve Equation t Generators 67600co1 [0,1,0,-3813,89363] 1 [266:169:8] 67600co2 [0,1,0,-43333,-3457037] 1 [-133255038:67165163:1191016]
67600cp (2 curves)	1	2- 5+ 13-	2-  1 5+ -2  0 13-  2 -4
Curve Equation t Generators 67600cp1 [0,1,0,-644453,198908243] 1 [1681424:7880639:4096] 67600cp2 [0,1,0,-7323333,-7565817037] 1 [-489867896093812684948912:2053979694437969951079323:329192772583268962304]
67600cq (2 curves)	1	2- 5+ 13-	2- -1 5+  3  0 13-  3 -6
Curve Equation t Generators 67600cq1 [0,-1,0,201392,106507712] 1 [-3123582:2904434:9261] 67600cq2 [0,-1,0,-21768608,-39738284288] 1 [2391268538313371803787645574:16766460475838663677225223462:441221141567440173064923]
67600cr (2 curves)	1	2- 5+ 13-	2- -1 5+ -3  0 13-  3  6
Curve Equation t Generators 67600cr1 [0,-1,0,1192,48112] 1 [-4:208:1] 67600cr2 [0,-1,0,-128808,-18047888] 1 [38892:1424384:27]
67600cs (2 curves)	1	2- 5+ 13-	2-  2 5+  0  0 13- -6  0
Curve Equation t Generators 67600cs1 [0,-1,0,-4632008,1469526512] 2 [-667044381916:-11967739032768:310288733] 67600cs2 [0,-1,0,-39784008,-95549993488] 2 [-191848568103480388356942:-1125016959968743924700866:49760544181701757221]
67600ct (2 curves)	1	2- 5+ 13-	2-  2 5+  0  0 13- -6  0
Curve Equation t Generators 67600ct1 [0,-1,0,-27408,677312] 2 [737:19500:1] 67600ct2 [0,-1,0,-235408,-43418688] 2 [21819:462500:27]
67600cu (1 curve)	1	2- 5+ 13-	2- -2 5+  5 -3 13-  5  4
Curve Equation t Generators 67600cu1 [0,1,0,25632,-128972] 1 [37420:733798:125]
67600cv (1 curve)	1	2- 5+ 13-	2- -2 5+ -5  3 13-  5 -4
Curve Equation t Generators 67600cv1 [0,1,0,152,-12] 1 [4:26:1]
67600cw (1 curve)	1	2- 5- 13+	2-  0 5- -3  3 13+ -1  4
Curve Equation t Generators 67600cw1 [0,0,0,4225,109850] 1 [130:1690:1]
67600cx (1 curve)	1	2- 5- 13+	2-  1 5-  2 -2 13+  2  0
Curve Equation t Generators 67600cx1 [0,1,0,-56333,3439463] 1 [-13:2042:1]
67600cy (1 curve)	1	2- 5- 13+	2-  1 5- -4  1 13+ -7 -3
Curve Equation t Generators 67600cy1 [0,1,0,32392,-24762412] 1 [12614:1416896:1]
67600cz (2 curves)	1	2- 5- 13+	2- -1 5-  2  2 13+  2  0
Curve Equation t Generators 67600cz1 [0,-1,0,-1374533,620728237] 1 [892716:389207:1331] 67600cz2 [0,-1,0,-6647333,-6070454963] 1 [-1178019115678890331396:-17591069399468726696717:902994504356614879]
67600da (4 curves)	1	2- 5- 13+	2- -1 5-  2 -3 13+ -3  5
Curve Equation t Generators 67600da1 [0,-1,0,-1408,240512] 1 [178:2366:1] 67600da2 [0,-1,0,-339408,76222912] 1 [282:1690:1] 67600da3 [0,-1,0,-204208,-42753088] 1 [25339958:594502454:29791] 67600da4 [0,-1,0,1485792,315526912] 1 [7042:599950:1]
67600db (2 curves)	1	2- 5- 13+	2- -1 5- -4 -6 13+  6 -4
Curve Equation t Generators 67600db1 [0,-1,0,-225333,-38168963] 1 [-212:169:1] 67600db2 [0,-1,0,-3605333,2628651037] 1 [-108:54925:1]
67600dc (2 curves)	1	2- 5- 13+	2-  2 5- -1  3 13+  3 -4
Curve Equation t Generators 67600dc1 [0,-1,0,-69008,-7060288] 1 [1355922:57842954:729] 67600dc2 [0,-1,0,268992,-33829888] 1 [13854:417430:27]
67600dd (2 curves)	1	2- 5- 13+	2-  2 5-  5 -3 13+  3 -4
Curve Equation t Generators 67600dd1 [0,-1,0,-8823208,12757644912] 1 [303626862:15480223226:250047] 67600dd2 [0,-1,0,-765943208,8159368844912] 1 [252534:36360350:27]
67600de (1 curve)	1	2- 5- 13+	2- -3 5-  0 -3 13+ -7  1
Curve Equation t Generators 67600de1 [0,0,0,-1499875,-711278750] 1 [1625:33800:1]
67600df (2 curves)	0	2- 5- 13-	2- -1 5-  2  0 13- -2 -4
Curve Equation t 67600df1 [0,-1,0,-292933,-60409363] 1 67600df2 [0,-1,0,-16111333,24895753037] 1
67600dg (2 curves)	0	2- 5- 13-	2- -1 5- -2  0 13- -2  4
Curve Equation t 67600dg1 [0,-1,0,-1733,-26963] 1 67600dg2 [0,-1,0,-95333,11361037] 1
67600dh (2 curves)	0	2- 5- 13-	2-  2 5-  0  2 13-  0 -6
Curve Equation t 67600dh1 [0,-1,0,-9208,276912] 2 67600dh2 [0,-1,0,-139208,20036912] 2
67600di (2 curves)	0	2- 5- 13-	2-  2 5-  0 -2 13-  0  6
Curve Equation t 67600di1 [0,-1,0,-1556208,602150912] 2 67600di2 [0,-1,0,-23526208,43926990912] 2
67600dj (1 curve)	0	2- 5- 13-	2-  2 5-  5  3 13- -5 -4
Curve Equation t 67600dj1 [0,-1,0,3792,-9088] 1
67600dk (1 curve)	0	2- 5- 13-	2-  2 5- -5 -3 13- -5  4
Curve Equation t 67600dk1 [0,-1,0,640792,-17403088] 1
67600dl (2 curves)	2	2- 5- 13-	2- -2 5-  0  2 13-  0 -6
Curve Equation t Generators 67600dl1 [0,1,0,-368,2068] 2 [-12:70:1]&[-6:64:1] 67600dl2 [0,1,0,-5568,158068] 2 [-78:352:1]&[-22:520:1]
67600dm (2 curves)	0	2- 5- 13-	2- -2 5-  0 -2 13-  0  6
Curve Equation t 67600dm1 [0,1,0,-62248,4792308] 2 67600dm2 [0,1,0,-941048,351039508] 2

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

Part of Computational Number Theory
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