Cremona's table of elliptic curves

83600 = 2⁴ · 5² · 11 · 19

Class	r	Atkin-Lehner	Eigenvalues
83600a (2 curves)	1	2+ 5+ 11+ 19+	2+  0 5+ -2 11+ -6 -6 19+
Curve Equation t Generators 83600a1 [0,0,0,-226934075,-1315823479750] 2 [57513376930210:10343748473546875:1473760072] 83600a2 [0,0,0,-226309075,-1323431604750] 2 [5057560709551995360216990:909710439266438462216276325:129606915352770108856]
83600b (2 curves)	1	2+ 5+ 11+ 19+	2+  0 5+  4 11+ -6  0 19+
Curve Equation t Generators 83600b1 [0,0,0,425,9750] 2 [34:252:1] 83600b2 [0,0,0,-5075,125250] 2 [11:266:1]
83600c (2 curves)	1	2+ 5+ 11+ 19+	2+  2 5+  4 11+ -4 -6 19+
Curve Equation t Generators 83600c1 [0,-1,0,-4883,-129238] 2 [682:17700:1] 83600c2 [0,-1,0,-2508,-257488] 2 [1177356:30613625:1728]
83600d (1 curve)	1	2+ 5+ 11+ 19+	2+ -2 5+  1 11+ -4  2 19+
Curve Equation t Generators 83600d1 [0,1,0,-648,-6572] 1 [84:734:1]
83600e (2 curves)	1	2+ 5+ 11+ 19+	2+ -2 5+ -2 11+  2  0 19+
Curve Equation t Generators 83600e1 [0,1,0,-1783,-27312] 2 [-28:38:1] 83600e2 [0,1,0,-27908,-1803812] 2 [403:7250:1]
83600f (2 curves)	1	2+ 5+ 11+ 19+	2+ -2 5+ -2 11+  2 -4 19+
Curve Equation t Generators 83600f1 [0,1,0,-652783,202780188] 2 [392:2698:1] 83600f2 [0,1,0,-678908,185642188] 2 [2586:2059:8]
83600g (1 curve)	1	2+ 5+ 11+ 19+	2+  3 5+ -2 11+ -3  6 19+
Curve Equation t Generators 83600g1 [0,0,0,-2989075,-2442172750] 1 [36281505655641465:1741897917169509950:10681430926167]
83600h (4 curves)	2	2+ 5+ 11+ 19-	2+  0 5+  0 11+ -2 -2 19-
Curve Equation t Generators 83600h1 [0,0,0,2950,14875] 2 [15:250:1]&[146370:19798625:8] 83600h2 [0,0,0,-12175,120750] 4 [-71:792:1]&[-66:798:1] 83600h3 [0,0,0,-116675,-15240750] 2 [-205:250:1]&[395:550:1] 83600h4 [0,0,0,-149675,22258250] 2 [-245:6650:1]&[235:250:1]
83600i (1 curve)	0	2+ 5+ 11+ 19-	2+  1 5+  2 11+  5 -2 19-
Curve Equation t 83600i1 [0,1,0,-8,43988] 1
83600j (1 curve)	0	2+ 5+ 11+ 19-	2+  1 5+  5 11+ -3  3 19-
Curve Equation t 83600j1 [0,1,0,6592,255188] 1
83600k (2 curves)	0	2+ 5+ 11+ 19-	2+  2 5+  0 11+  2  4 19-
Curve Equation t 83600k1 [0,-1,0,-1408,15312] 2 83600k2 [0,-1,0,3592,95312] 2
83600l (2 curves)	0	2+ 5+ 11+ 19-	2+ -2 5+  2 11+  2  4 19-
Curve Equation t 83600l1 [0,1,0,-2783,-6812] 2 83600l2 [0,1,0,-28908,1874188] 2
83600m (2 curves)	0	2+ 5+ 11+ 19-	2+ -2 5+  2 11+ -6  0 19-
Curve Equation t 83600m1 [0,1,0,-25525783,49458911688] 2 83600m2 [0,1,0,-408021908,3172157276188] 2
83600n (2 curves)	0	2+ 5+ 11+ 19-	2+ -2 5+ -4 11+  4  6 19-
Curve Equation t 83600n1 [0,1,0,-6883,-3613512] 2 83600n2 [0,1,0,-397508,-95801012] 2
83600o (4 curves)	2	2+ 5+ 11- 19+	2+  0 5+ -4 11- -2 -2 19+
Curve Equation t Generators 83600o1 [0,0,0,-1775,28750] 2 [30:50:1]&[61:384:1] 83600o2 [0,0,0,-2275,11250] 4 [-45:150:1]&[-31:228:1] 83600o3 [0,0,0,8725,88250] 2 [-1:282:1]&[215:3450:1] 83600o4 [0,0,0,-21275,-1185750] 2 [-81:78:1]&[-79:44:1]
83600p (2 curves)	0	2+ 5+ 11- 19+	2+  2 5+  2 11-  2  8 19+
Curve Equation t 83600p1 [0,-1,0,-1908,-30688] 2 83600p2 [0,-1,0,-4408,69312] 2
83600q (1 curve)	1	2+ 5+ 11- 19-	2+  1 5+  2 11- -4  2 19-
Curve Equation t Generators 83600q1 [0,1,0,-15433,741763] 1 [-18:1007:1]
83600r (1 curve)	1	2+ 5+ 11- 19-	2+  1 5+ -3 11-  1  7 19-
Curve Equation t Generators 83600r1 [0,1,0,-129808,-18113612] 1 [588:10450:1]
83600s (2 curves)	1	2+ 5+ 11- 19-	2+  2 5+  0 11- -4  2 19-
Curve Equation t Generators 83600s1 [0,-1,0,-4883,-144238] 2 [180422:1718100:1331] 83600s2 [0,-1,0,-80508,-8765488] 2 [1457:54450:1]
83600t (2 curves)	1	2+ 5+ 11- 19-	2+ -2 5+  2 11-  2 -4 19-
Curve Equation t Generators 83600t1 [0,1,0,-5908,-19812] 2 [82:232:1] 83600t2 [0,1,0,-68408,-6894812] 2 [-146:44:1]
83600u (2 curves)	1	2+ 5+ 11- 19-	2+ -2 5+ -4 11- -4  2 19-
Curve Equation t Generators 83600u1 [0,1,0,5383117,-69108821012] 2 [42388:8736200:1] 83600u2 [0,1,0,-223382508,-1244049071012] 2 [21543:-1985500:1]
83600v (1 curve)	0	2+ 5- 11+ 19+	2+  2 5- -1 11+  4 -2 19+
Curve Equation t 83600v1 [0,-1,0,-16208,-789088] 1
83600w (2 curves)	0	2+ 5- 11+ 19+	2+  2 5-  2 11+ -4 -4 19+
Curve Equation t 83600w1 [0,-1,0,-803,7502] 2 83600w2 [0,-1,0,-3828,-83248] 2
83600x (2 curves)	0	2+ 5- 11+ 19+	2+ -2 5- -2 11+  4  4 19+
Curve Equation t 83600x1 [0,1,0,-20083,897588] 2 83600x2 [0,1,0,-95708,-10597412] 2
83600y (2 curves)	1	2+ 5- 11+ 19-	2+  0 5-  2 11+ -2  0 19-
Curve Equation t Generators 83600y1 [0,0,0,-170,-725] 2 [15:10:1] 83600y2 [0,0,0,305,-4050] 2 [2430:119790:1]
83600z (2 curves)	1	2+ 5- 11+ 19-	2+  0 5- -2 11+  2  0 19-
Curve Equation t Generators 83600z1 [0,0,0,-4250,-90625] 2 [475:10250:1] 83600z2 [0,0,0,7625,-506250] 2 [3762:82779:8]
83600ba (1 curve)	1	2+ 5- 11+ 19-	2+  1 5-  2 11+  3  2 19-
Curve Equation t Generators 83600ba1 [0,1,0,-16208,-1158412] 1 [158:500:1]
83600bb (1 curve)	1	2+ 5- 11+ 19-	2+ -1 5- -2 11+ -3 -2 19-
Curve Equation t Generators 83600bb1 [0,-1,0,-648,-9008] 1 [42:190:1]
83600bc (2 curves)	2	2- 5+ 11+ 19+	2-  0 5+  2 11+  2 -6 19+
Curve Equation t Generators 83600bc1 [0,0,0,-1475,-18750] 2 [-25:50:1]&[129:1392:1] 83600bc2 [0,0,0,2525,-102750] 2 [41:264:1]&[55:450:1]
83600bd (2 curves)	0	2- 5+ 11+ 19+	2-  1 5+  2 11+  1 -6 19+
Curve Equation t 83600bd1 [0,1,0,17592,-15452812] 1 83600bd2 [0,1,0,-158408,418563188] 1
83600be (2 curves)	0	2- 5+ 11+ 19+	2-  1 5+ -4 11+ -2  0 19+
Curve Equation t 83600be1 [0,1,0,-10933,-518237] 1 83600be2 [0,1,0,77067,3001763] 1
83600bf (1 curve)	0	2- 5+ 11+ 19+	2- -1 5+ -3 11+  3 -5 19+
Curve Equation t 83600bf1 [0,-1,0,-1338008,-603465488] 1
83600bg (2 curves)	0	2- 5+ 11+ 19+	2-  2 5+  0 11+ -4  2 19+
Curve Equation t 83600bg1 [0,-1,0,67,1112] 2 83600bg2 [0,-1,0,-1308,17612] 2
83600bh (1 curve)	0	2- 5+ 11+ 19+	2-  2 5+ -3 11+  0 -2 19+
Curve Equation t 83600bh1 [0,-1,0,165032,-18709008] 1
83600bi (4 curves)	0	2- 5+ 11+ 19+	2- -2 5+ -4 11+ -2  0 19+
Curve Equation t 83600bi1 [0,1,0,-209408,-36948812] 2 83600bi2 [0,1,0,-189408,-44268812] 2 83600bi3 [0,1,0,-495408,82511188] 2 83600bi4 [0,1,0,1504592,582511188] 2
83600bj (1 curve)	0	2- 5+ 11+ 19+	2-  3 5+  1 11+  7  3 19+
Curve Equation t 83600bj1 [0,0,0,-2275,49250] 1
83600bk (1 curve)	1	2- 5+ 11+ 19-	2- -1 5+ -1 11+ -1 -1 19-
Curve Equation t Generators 83600bk1 [0,-1,0,-19008,-5823488] 1 [2112:96800:1]
83600bl (2 curves)	1	2- 5+ 11+ 19-	2- -1 5+ -2 11+  1  2 19-
Curve Equation t Generators 83600bl1 [0,-1,0,-194008,-32873488] 1 [8012:716000:1] 83600bl2 [0,-1,0,1385992,442646512] 1 [1412:72200:1]
83600bm (1 curve)	1	2- 5+ 11+ 19-	2-  2 5+ -1 11+  0 -2 19-
Curve Equation t Generators 83600bm1 [0,-1,0,-2608,-57408] 1 [78497922:1071865434:389017]
83600bn (2 curves)	1	2- 5+ 11+ 19-	2-  2 5+  4 11+  4 -4 19-
Curve Equation t Generators 83600bn1 [0,-1,0,-397419133,1761138357012] 2 [44779208332927479412406510724936570249395301774:7467556532715233616408069317479578458071112615625:1203161721054316608083891323712347061069912] 83600bn2 [0,-1,0,-2833315508,-56797810497988] 2 [22607721139905543076889175527567601818133674655940009630685071166243351467479187716263761405722:-484376843767858527036946627560475146523241387883253685661374740091974932863554202251886611328125:367479274394831976673244452671544278861511204693405154971283064355144147157023878735220296]
83600bo (2 curves)	1	2- 5+ 11+ 19-	2-  2 5+ -4 11+ -4 -4 19-
Curve Equation t Generators 83600bo1 [0,-1,0,-15133,721512] 2 [2604:-10450:27] 83600bo2 [0,-1,0,-16508,584012] 2 [37:150:1]
83600bp (4 curves)	1	2- 5+ 11- 19+	2-  0 5+  0 11- -2  6 19+
Curve Equation t Generators 83600bp1 [0,0,0,-77675,4324250] 2 [82165:23552000:1] 83600bp2 [0,0,0,-589675,-171291750] 4 [-5942602:-5478726:12167] 83600bp3 [0,0,0,18325,-507515750] 2 [69015:3440800:27] 83600bp4 [0,0,0,-9389675,-11074491750] 2 [-365535674470986:-6226046728518:206529873031]
83600bq (4 curves)	1	2- 5+ 11- 19+	2-  0 5+  0 11- -2  6 19+
Curve Equation t Generators 83600bq1 [0,0,0,-392963675,2998311314250] 2 [141970:10161875:8] 83600bq2 [0,0,0,-392965675,2998279268250] 4 [50812806430:3637010203125:2863288] 83600bq3 [0,0,0,-379247675,3217314574250] 2 [124815:33754600:27] 83600bq4 [0,0,0,-406715675,2777193018250] 2 [422842753511620590:-27462972323943730925:23251619396088]
83600br (1 curve)	1	2- 5+ 11- 19+	2-  0 5+ -3 11- -2  0 19+
Curve Equation t Generators 83600br1 [0,0,0,85,90] 1 [-1:2:1]
83600bs (1 curve)	1	2- 5+ 11- 19+	2-  1 5+ -1 11-  5  3 19+
Curve Equation t Generators 83600bs1 [0,1,0,151627592,2415985295188] 1 [-11944062036:127840666250:1225043]
83600bt (1 curve)	1	2- 5+ 11- 19+	2- -1 5+  0 11-  2  4 19+
Curve Equation t Generators 83600bt1 [0,-1,0,-133,6137] 1 [-19:38:1]
83600bu (1 curve)	1	2- 5+ 11- 19+	2- -1 5+ -3 11- -1  7 19+
Curve Equation t Generators 83600bu1 [0,-1,0,26392,249712] 1 [2:550:1]
83600bv (2 curves)	1	2- 5+ 11- 19+	2- -2 5+  2 11-  2  0 19+
Curve Equation t Generators 83600bv1 [0,1,0,-12408,287188] 2 [3:500:1] 83600bv2 [0,1,0,-172408,27487188] 2 [262:-608:1]
83600bw (4 curves)	1	2- 5+ 11- 19+	2- -2 5+  2 11- -2  0 19+
Curve Equation t Generators 83600bw1 [0,1,0,-631408,-193312812] 2 [5663:421750:1] 83600bw2 [0,1,0,-671408,-167472812] 2 [-302:2800:1] 83600bw3 [0,1,0,-1277408,262307188] 2 [-198:22528:1] 83600bw4 [0,1,0,-17277408,27622307188] 2 [-582:193600:1]
83600bx (4 curves)	0	2- 5+ 11- 19-	2-  0 5+  0 11- -2  2 19-
Curve Equation t 83600bx1 [0,0,0,-4601675,-18173471750] 2 83600bx2 [0,0,0,-135673675,-606293535750] 4 83600bx3 [0,0,0,-199673675,24042464250] 4 83600bx4 [0,0,0,-2168825675,-38876313631750] 2
83600by (2 curves)	0	2- 5+ 11- 19-	2-  0 5+  0 11- -2 -4 19-
Curve Equation t 83600by1 [0,0,0,13925,530250] 2 83600by2 [0,0,0,-74075,4842250] 2
83600bz (2 curves)	0	2- 5+ 11- 19-	2-  0 5+ -2 11-  0  6 19-
Curve Equation t 83600bz1 [0,0,0,-45200,2030375] 2 83600bz2 [0,0,0,-332575,-72399750] 2
83600ca (2 curves)	0	2- 5+ 11- 19-	2-  0 5+  4 11- -6  0 19-
Curve Equation t 83600ca1 [0,0,0,-1501075,709127250] 2 83600ca2 [0,0,0,-24029075,45337095250] 2
83600cb (2 curves)	0	2- 5+ 11- 19-	2-  2 5+  2 11-  6  4 19-
Curve Equation t 83600cb1 [0,-1,0,-213408,37997312] 2 83600cb2 [0,-1,0,-253408,22797312] 2
83600cc (2 curves)	2	2- 5+ 11- 19-	2- -2 5+ -2 11- -6  0 19-
Curve Equation t Generators 83600cc1 [0,1,0,-2408,35188] 2 [-52:150:1]&[-12:250:1] 83600cc2 [0,1,0,-12408,-504812] 2 [-66:176:1]&[-58:152:1]
83600cd (1 curve)	0	2- 5+ 11- 19-	2-  3 5+  3 11- -5 -1 19-
Curve Equation t 83600cd1 [0,0,0,-817675,4351624250] 1
83600ce (1 curve)	0	2- 5+ 11- 19-	2- -3 5+ -3 11-  1 -1 19-
Curve Equation t 83600ce1 [0,0,0,-1520644075,-26448026507750] 1
83600cf (2 curves)	1	2- 5- 11+ 19+	2-  0 5-  2 11+  2 -2 19+
Curve Equation t Generators 83600cf1 [0,0,0,-15500,-740625] 2 [5249:380182:1] 83600cf2 [0,0,0,-22375,-18750] 2 [55894102:-4047981561:10648]
83600cg (2 curves)	1	2- 5- 11+ 19+	2-  0 5-  2 11+  2  4 19+
Curve Equation t Generators 83600cg1 [0,0,0,-32099875,164394281250] 2 [131673979537533500895:-14107589027207309164544:10147139057487375] 83600cg2 [0,0,0,-687459875,6930986281250] 2 [313609173875:-5906730240000:22665187]
83600ch (2 curves)	1	2- 5- 11+ 19+	2-  0 5- -2 11+ -2  2 19+
Curve Equation t Generators 83600ch1 [0,0,0,-620,-5925] 2 [29:22:1] 83600ch2 [0,0,0,-895,-150] 2 [7250:617310:1]
83600ci (2 curves)	1	2- 5- 11+ 19+	2-  0 5- -2 11+ -2 -4 19+
Curve Equation t Generators 83600ci1 [0,0,0,-1283995,1315154250] 2 [-630:43290:1] 83600ci2 [0,0,0,-27498395,55447890250] 2 [19005:2529280:1]
83600cj (2 curves)	1	2- 5- 11+ 19+	2-  1 5-  2 11+ -1 -2 19+
Curve Equation t Generators 83600cj1 [0,1,0,-11648,509108] 1 [68:190:1] 83600cj2 [0,1,0,27952,-32464492] 1 [166451308:8191891990:68921]
83600ck (2 curves)	1	2- 5- 11+ 19+	2- -1 5- -2 11+  1  2 19+
Curve Equation t Generators 83600ck1 [0,-1,0,-291208,64220912] 1 [292:-2000:1] 83600ck2 [0,-1,0,698792,-4059459088] 1 [14835428:596608000:6859]
83600cl (2 curves)	1	2- 5- 11+ 19+	2-  2 5-  4 11+ -2  2 19+
Curve Equation t Generators 83600cl1 [0,-1,0,4912,39872] 2 [2186:37275:8] 83600cl2 [0,-1,0,-20688,347072] 2 [4584:35200:27]
83600cm (1 curve)	1	2- 5- 11+ 19+	2- -2 5-  3 11+  0  2 19+
Curve Equation t Generators 83600cm1 [0,1,0,4125792,-2330374412] 1 [605587384545253548:7234274064637184111258:4243659659]
83600cn (2 curves)	1	2- 5- 11+ 19+	2- -2 5- -4 11+  2 -2 19+
Curve Equation t Generators 83600cn1 [0,1,0,122792,5229588] 2 [83:4000:1] 83600cn2 [0,1,0,-517208,42349588] 2 [-42:8000:1]
83600co (1 curve)	1	2- 5- 11+ 19+	2-  3 5- -2 11+ -5  2 19+
Curve Equation t Generators 83600co1 [0,0,0,9125,106250] 1 [136575:2111750:729]
83600cp (1 curve)	1	2- 5- 11+ 19+	2- -3 5-  2 11+  5 -2 19+
Curve Equation t Generators 83600cp1 [0,0,0,365,850] 1 [25:160:1]
83600cq (1 curve)	0	2- 5- 11+ 19-	2- -2 5-  1 11+  0  2 19-
Curve Equation t 83600cq1 [0,1,0,-65208,-7306412] 1
83600cr (2 curves)	0	2- 5- 11- 19+	2-  0 5-  2 11- -6  8 19+
Curve Equation t 83600cr1 [0,0,0,-40195,6331650] 2 83600cr2 [0,0,0,-814595,282792450] 2
83600cs (2 curves)	0	2- 5- 11- 19+	2-  0 5- -2 11-  6 -8 19+
Curve Equation t 83600cs1 [0,0,0,-1004875,791456250] 2 83600cs2 [0,0,0,-20364875,35349056250] 2
83600ct (1 curve)	0	2- 5- 11- 19+	2-  0 5-  3 11-  2  0 19+
Curve Equation t 83600ct1 [0,0,0,2125,11250] 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