Cremona's table of elliptic curves

21450 = 2 · 3 · 5² · 11 · 13

Class	r	Atkin-Lehner	Eigenvalues
21450a (4 curves)	1	2+ 3+ 5+ 11+ 13+	2+ 3+ 5+  0 11+ 13+ -6  4
Curve Equation t Generators 21450a1 [1,1,0,27350,-3747500] 2 [12644:1415630:1] 21450a2 [1,1,0,-260650,-44355500] 4 [-204:718:1] 21450a3 [1,1,0,-1118650,411242500] 2 [771:2411:1] 21450a4 [1,1,0,-4010650,-3093105500] 2 [50595:11346290:1]
21450b (1 curve)	1	2+ 3+ 5+ 11+ 13+	2+ 3+ 5+ -3 11+ 13+  0 -5
Curve Equation t Generators 21450b1 [1,1,0,-150,750] 1 [5:10:1]
21450c (4 curves)	1	2+ 3+ 5+ 11+ 13+	2+ 3+ 5+  4 11+ 13+  0  2
Curve Equation t Generators 21450c1 [1,1,0,22060725,-739086199875] 2 [9939689792507784849384190:1651362089812140924355595905:355944539247410249317] 21450c2 [1,1,0,-1104339275,-13718593399875] 2 [207852489082979208695696102485222535793056355:10196634663457046210064816040883143577590719385:5280353842570029894690758070645911080839] 21450c3 [1,1,0,-5545555275,-158981090551875] 2 [146428846554999887319952276808196322438451015829858888873960829701650:44663156056894433810008050692577927669108118766119804965222227551627175:1040273114473505321946589577063270922459163755274545446101206083] 21450c4 [1,1,0,-88733055275,-10173674653051875] 2 [3046704177436099014237385018654573798334348658205170822414662296891397288793972083159541025719686220628930751903204284434956132804314575:1338459953457871342787725034386719334460318201958357785635953982154778113958952877409848797626886717957716557976983757295003804306443586525:6853760435297887664868331196805221394284859629933658892324764143944427002057085051687251132042217906761430604202244245604213321379]
21450d (8 curves)	1	2+ 3+ 5+ 11+ 13+	2+ 3+ 5+  4 11+ 13+  6 -4
Curve Equation t Generators 21450d1 [1,1,0,-285500,-56286000] 2 [-465685:1514455:1331] 21450d2 [1,1,0,-797500,201250000] 4 [-945:11060:1] 21450d3 [1,1,0,-22845500,-42038526000] 2 [17064589372061672:-1503286918711251372:1658536153253] 21450d4 [1,1,0,2010500,1304794000] 2 [-166887:5074028:343] 21450d5 [1,1,0,-11797500,15590250000] 2 [2000:-500:1] 21450d6 [1,1,0,-22847500,-42030800000] 4 [1827705045572:111775359344732:241804367] 21450d7 [1,1,0,-19552000,-54576768500] 2 [176000000125600695:-34651703166338429410:4501115240831] 21450d8 [1,1,0,-26175000,-28990327500] 2 [6050:181750:1]
21450e (2 curves)	1	2+ 3+ 5+ 11+ 13+	2+ 3+ 5+ -5 11+ 13+  0  2
Curve Equation t Generators 21450e1 [1,1,0,325,-4875] 1 [11:8:1] 21450e2 [1,1,0,-15425,-745125] 1 [161:908:1]
21450f (6 curves)	0	2+ 3+ 5+ 11- 13+	2+ 3+ 5+  0 11- 13+ -2  4
Curve Equation t 21450f1 [1,1,0,-71000,3144000] 2 21450f2 [1,1,0,-583000,-169400000] 4 21450f3 [1,1,0,-63000,-460080000] 2 21450f4 [1,1,0,-9295000,-10911296000] 4 21450f5 [1,1,0,-9262000,-10992575000] 2 21450f6 [1,1,0,-148720000,-698137121000] 2
21450g (2 curves)	0	2+ 3+ 5+ 11- 13+	2+ 3+ 5+  2 11- 13+  6 -4
Curve Equation t 21450g1 [1,1,0,7475,860125] 2 21450g2 [1,1,0,-102525,11530125] 2
21450h (4 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  0 11- 13-  6  4
Curve Equation t Generators 21450h1 [1,1,0,-1150,14500] 2 [24:26:1] 21450h2 [1,1,0,-1650,0] 4 [-25:175:1] 21450h3 [1,1,0,6600,8250] 2 [41:571:1] 21450h4 [1,1,0,-17900,-926250] 2 [-75:75:1]
21450i (2 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+ -1 11- 13- -4  6
Curve Equation t Generators 21450i1 [1,1,0,-144360025,668252897125] 1 [5839:153451:1] 21450i2 [1,1,0,408827225,-41942876529125] 1 [919721921:126511763189:24389]
21450j (1 curve)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  3 11- 13-  3  1
Curve Equation t Generators 21450j1 [1,1,0,308140,15523920] 1 [136:7676:1]
21450k (2 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+  4 11- 13- -4 -4
Curve Equation t Generators 21450k1 [1,1,0,-25,-875] 2 [14:35:1] 21450k2 [1,1,0,-1525,-23375] 2 [-24:23:1]
21450l (2 curves)	1	2+ 3+ 5+ 11- 13-	2+ 3+ 5+ -4 11- 13-  8 -6
Curve Equation t Generators 21450l1 [1,1,0,-8300,-750000] 2 [175:1700:1] 21450l2 [1,1,0,-184300,-30494000] 2 [-251:301:1]
21450m (1 curve)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5-  0 11+ 13+  0  7
Curve Equation t 21450m1 [1,1,0,3575,325] 1
21450n (1 curve)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5-  0 11+ 13+  3  0
Curve Equation t 21450n1 [1,1,0,-4175,-109275] 1
21450o (1 curve)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5-  1 11+ 13+ -2 -7
Curve Equation t 21450o1 [1,1,0,5485675,-1401157875] 1
21450p (1 curve)	0	2+ 3+ 5- 11+ 13+	2+ 3+ 5- -4 11+ 13+ -7  8
Curve Equation t 21450p1 [1,1,0,50,-3500] 1
21450q (2 curves)	1	2+ 3+ 5- 11- 13+	2+ 3+ 5-  2 11- 13+  2 -5
Curve Equation t Generators 21450q1 [1,1,0,-64500,-7200600] 1 [845:22870:1] 21450q2 [1,1,0,-103825,568847125] 1 [735:29470:1]
21450r (2 curves)	1	2+ 3+ 5- 11- 13+	2+ 3+ 5- -3 11- 13+  2  5
Curve Equation t Generators 21450r1 [1,1,0,-325320075,-2258605987875] 1 [168959754395:65880169486740:1092727] 21450r2 [1,1,0,-249083200,-3343740416000] 1 [1053921541456550750134302700610442576975673902142695:411418772938894345613837502633487951246560779661848840:6820192712256572917317723617647060973795074897]
21450s (1 curve)	0	2+ 3+ 5- 11- 13-	2+ 3+ 5- -1 11- 13-  6  1
Curve Equation t 21450s1 [1,1,0,-6200,264000] 1
21450t (1 curve)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+ -1 11+ 13+  8 -6
Curve Equation t 21450t1 [1,0,1,-14301,14864248] 1
21450u (2 curves)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+  2 11+ 13+  2  0
Curve Equation t 21450u1 [1,0,1,-45651,-3808802] 2 21450u2 [1,0,1,-733151,-241683802] 2
21450v (2 curves)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+  2 11+ 13+ -2  4
Curve Equation t 21450v1 [1,0,1,-3901,439448] 2 21450v2 [1,0,1,-113901,14739448] 2
21450w (4 curves)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+  4 11+ 13+ -6 -8
Curve Equation t 21450w1 [1,0,1,1624,-32602] 2 21450w2 [1,0,1,-10876,-332602] 4 21450w3 [1,0,1,-59626,5322398] 2 21450w4 [1,0,1,-162126,-25137602] 2
21450x (4 curves)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+ -4 11+ 13+  2  0
Curve Equation t 21450x1 [1,0,1,-2117207626,38462714137148] 2 21450x2 [1,0,1,-34117207626,2425534714137148] 4 21450x3 [1,0,1,-34359207626,2389378946137148] 2 21450x4 [1,0,1,-545875207626,155234426482137148] 2
21450y (1 curve)	0	2+ 3- 5+ 11+ 13+	2+ 3- 5+ -4 11+ 13+  4  1
Curve Equation t 21450y1 [1,0,1,-414701,-104529202] 1
21450z (4 curves)	1	2+ 3- 5+ 11+ 13-	2+ 3- 5+ -4 11+ 13- -2 -4
Curve Equation t Generators 21450z1 [1,0,1,-26676,1672498] 2 [122:426:1] 21450z2 [1,0,1,-34676,584498] 4 [-87:1759:1] 21450z3 [1,0,1,134324,4640498] 2 [238:6959:1] 21450z4 [1,0,1,-331676,-73071502] 2 [-312:409:1]
21450ba (2 curves)	1	2+ 3- 5+ 11- 13+	2+ 3- 5+  0 11- 13+  0  0
Curve Equation t Generators 21450ba1 [1,0,1,-57526,-5338552] 2 [2152:98111:1] 21450ba2 [1,0,1,-921526,-340570552] 2 [1477:38261:1]
21450bb (4 curves)	1	2+ 3- 5+ 11- 13+	2+ 3- 5+  0 11- 13+ -6  0
Curve Equation t Generators 21450bb1 [1,0,1,-3851,106598] 2 [-18:421:1] 21450bb2 [1,0,1,-64351,6277598] 4 [97:926:1] 21450bb3 [1,0,1,-67101,5711098] 2 [86:717:1] 21450bb4 [1,0,1,-1029601,402030098] 2 [586:-283:1]
21450bc (1 curve)	1	2+ 3- 5+ 11- 13+	2+ 3- 5+  2 11- 13+  6 -3
Curve Equation t Generators 21450bc1 [1,0,1,-81,388] 1 [8:12:1]
21450bd (2 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+ -2 11- 13-  4 -2
Curve Equation t 21450bd1 [1,0,1,-25193526,-48770930552] 2 21450bd2 [1,0,1,-403318526,-3117633430552] 2
21450be (1 curve)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  3 11- 13-  4 -2
Curve Equation t 21450be1 [1,0,1,-1151,15698] 1
21450bf (4 curves)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  4 11- 13- -2  4
Curve Equation t 21450bf1 [1,0,1,-1651,-18802] 2 21450bf2 [1,0,1,-9651,349198] 4 21450bf3 [1,0,1,5349,1339198] 2 21450bf4 [1,0,1,-152651,22943198] 2
21450bg (1 curve)	0	2+ 3- 5+ 11- 13-	2+ 3- 5+  4 11- 13- -5 -8
Curve Equation t 21450bg1 [1,0,1,-49475951,-175158556702] 1
21450bh (2 curves)	0	2+ 3- 5- 11+ 13-	2+ 3- 5-  0 11+ 13-  2  8
Curve Equation t 21450bh1 [1,0,1,3549,-2503202] 2 21450bh2 [1,0,1,-256451,-48783202] 2
21450bi (2 curves)	0	2+ 3- 5- 11- 13+	2+ 3- 5-  0 11- 13+ -6  0
Curve Equation t 21450bi1 [1,0,1,-828576,-655645202] 2 21450bi2 [1,0,1,-17468576,-28078365202] 2
21450bj (1 curve)	0	2+ 3- 5- 11- 13+	2+ 3- 5-  1 11- 13+  6  7
Curve Equation t 21450bj1 [1,0,1,-333076,78001298] 1
21450bk (1 curve)	2	2+ 3- 5- 11- 13+	2+ 3- 5- -5 11- 13+ -5 -5
Curve Equation t Generators 21450bk1 [1,0,1,-13151,581798] 1 [-123:646:1]&[-99:1006:1]
21450bl (1 curve)	1	2+ 3- 5- 11- 13-	2+ 3- 5-  3 11- 13- -1 -5
Curve Equation t Generators 21450bl1 [1,0,1,-1326,-25952] 1 [61:317:1]
21450bm (1 curve)	1	2+ 3- 5- 11- 13-	2+ 3- 5-  3 11- 13- -6 -5
Curve Equation t Generators 21450bm1 [1,0,1,-123201,16762798] 1 [452:7086:1]
21450bn (2 curves)	0	2- 3+ 5+ 11+ 13+	2- 3+ 5+  1 11+ 13+  0  5
Curve Equation t 21450bn1 [1,1,1,-2063,-310219] 1 21450bn2 [1,1,1,-416438,-103611469] 1
21450bo (4 curves)	0	2- 3+ 5+ 11+ 13+	2- 3+ 5+ -2 11+ 13+ -6 -4
Curve Equation t 21450bo1 [1,1,1,-14938,-8092969] 2 21450bo2 [1,1,1,-702438,-225342969] 2 21450bo3 [1,1,1,-3549313,-2575267969] 2 21450bo4 [1,1,1,-56789313,-164744307969] 2
21450bp (4 curves)	0	2- 3+ 5+ 11+ 13+	2- 3+ 5+  4 11+ 13+  0 -4
Curve Equation t 21450bp1 [1,1,1,8987,239531] 2 21450bp2 [1,1,1,-45013,2075531] 2 21450bp3 [1,1,1,-93388,-14707219] 2 21450bp4 [1,1,1,-1629388,-801139219] 2
21450bq (1 curve)	1	2- 3+ 5+ 11+ 13-	2- 3+ 5+ -1 11+ 13- -4  1
Curve Equation t Generators 21450bq1 [1,1,1,249412,-39829219] 1 [365:9817:1]
21450br (2 curves)	1	2- 3+ 5+ 11+ 13-	2- 3+ 5+  4 11+ 13- -4 -2
Curve Equation t Generators 21450br1 [1,1,1,-2938,194531] 2 [390:3101:8] 21450br2 [1,1,1,-71688,7344531] 2 [34530:-8273:216]
21450bs (2 curves)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+  0 11- 13+  4 -2
Curve Equation t Generators 21450bs1 [1,1,1,-16688,1107281] 2 [65:517:1] 21450bs2 [1,1,1,-291688,60507281] 2 [-481:9717:1]
21450bt (2 curves)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+  1 11- 13+  0  2
Curve Equation t Generators 21450bt1 [1,1,1,-2599663,1612249781] 1 [1019:4242:1] 21450bt2 [1,1,1,-2018038,2353388531] 1 [-31:49167:1]
21450bu (2 curves)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+  1 11- 13+  0 -7
Curve Equation t Generators 21450bu1 [1,1,1,-101838,-49047219] 1 [21990:1133001:8] 21450bu2 [1,1,1,-13800963,-19739701719] 1 [113762881230:471152327589:26463592]
21450bv (1 curve)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+ -3 11- 13+  1 -5
Curve Equation t Generators 21450bv1 [1,1,1,-53,-229] 1 [11:20:1]
21450bw (2 curves)	1	2- 3+ 5+ 11- 13+	2- 3+ 5+ -4 11- 13+  0  2
Curve Equation t Generators 21450bw1 [1,1,1,-163,-1219] 2 [55:372:1] 21450bw2 [1,1,1,-2913,-61719] 2 [550:1821:8]
21450bx (4 curves)	0	2- 3+ 5+ 11- 13-	2- 3+ 5+  0 11- 13- -2 -4
Curve Equation t 21450bx1 [1,1,1,-838,116531] 2 21450bx2 [1,1,1,-41338,3194531] 4 21450bx3 [1,1,1,-70588,-1953469] 2 21450bx4 [1,1,1,-660088,206144531] 2
21450by (1 curve)	0	2- 3+ 5+ 11- 13-	2- 3+ 5+  5 11- 13-  5 -5
Curve Equation t 21450by1 [1,1,1,-328763,72724781] 1
21450bz (2 curves)	1	2- 3+ 5- 11+ 13+	2- 3+ 5-  0 11+ 13+ -2  8
Curve Equation t Generators 21450bz1 [1,1,1,142,-19969] 2 [51:325:1] 21450bz2 [1,1,1,-10258,-394369] 2 [-65:87:1]
21450ca (1 curve)	0	2- 3+ 5- 11+ 13-	2- 3+ 5-  4 11+ 13- -4  1
Curve Equation t 21450ca1 [1,1,1,-16588,-842869] 1
21450cb (1 curve)	0	2- 3+ 5- 11- 13+	2- 3+ 5- -3 11- 13+  6 -5
Curve Equation t 21450cb1 [1,1,1,-4928,132131] 1
21450cc (1 curve)	0	2- 3+ 5- 11- 13+	2- 3+ 5- -4 11- 13+  5 -8
Curve Equation t 21450cc1 [1,1,1,-1979038,-1402060069] 1
21450cd (2 curves)	1	2- 3+ 5- 11- 13-	2- 3+ 5-  0 11- 13-  6  0
Curve Equation t Generators 21450cd1 [1,1,1,-33143,-5258419] 2 [315:3802:1] 21450cd2 [1,1,1,-698743,-224906419] 2 [-485:682:1]
21450ce (1 curve)	1	2- 3+ 5- 11- 13-	2- 3+ 5- -1 11- 13- -6  7
Curve Equation t Generators 21450ce1 [1,1,1,-13323,618681] 1 [405:7662:1]
21450cf (1 curve)	1	2- 3+ 5- 11- 13-	2- 3+ 5- -2 11- 13- -6 -3
Curve Equation t Generators 21450cf1 [1,1,1,-2013,48531] 1 [-15:282:1]
21450cg (4 curves)	1	2- 3- 5+ 11+ 13+	2- 3- 5+ -4 11+ 13+ -6  4
Curve Equation t Generators 21450cg1 [1,0,0,537,-272583] 2 [72:339:1] 21450cg2 [1,0,0,-59963,-5536083] 4 [-134:379:1] 21450cg3 [1,0,0,-134213,10873167] 2 [3878:59915:8] 21450cg4 [1,0,0,-953713,-358567333] 2 [11686:289807:8]
21450ch (1 curve)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  0 11+ 13-  0  7
Curve Equation t 21450ch1 [1,0,0,89362,-138108] 1
21450ci (1 curve)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  0 11+ 13- -3  0
Curve Equation t 21450ci1 [1,0,0,-104388,-13450608] 1
21450cj (4 curves)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  0 11+ 13- -6  4
Curve Equation t 21450cj1 [1,0,0,-3313,-281383] 4 21450cj2 [1,0,0,-87813,-9998883] 4 21450cj3 [1,0,0,-123563,-1097133] 2 21450cj4 [1,0,0,-1404063,-640482633] 2
21450ck (2 curves)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  2 11+ 13-  4  6
Curve Equation t 21450ck1 [1,0,0,-1086813,623259117] 2 21450ck2 [1,0,0,-19388063,32851760367] 2
21450cl (1 curve)	0	2- 3- 5+ 11+ 13-	2- 3- 5+  4 11+ 13-  7  8
Curve Equation t 21450cl1 [1,0,0,2,-28] 1
21450cm (1 curve)	0	2- 3- 5+ 11+ 13-	2- 3- 5+ -5 11+ 13-  4 -1
Curve Equation t 21450cm1 [1,0,0,13062062,-8750496508] 1
21450cn (4 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+  0 11- 13+  2 -4
Curve Equation t 21450cn1 [1,0,0,202037,-132957583] 2 21450cn2 [1,0,0,-2997963,-1844957583] 4 21450cn3 [1,0,0,-10257963,10533342417] 2 21450cn4 [1,0,0,-46937963,-123778457583] 2
21450co (4 curves)	0	2- 3- 5+ 11- 13+	2- 3- 5+  4 11- 13+ -2  0
Curve Equation t 21450co1 [1,0,0,-61213,-13701583] 2 21450co2 [1,0,0,-1311213,-577451583] 4 21450co3 [1,0,0,-1648713,-257164083] 2 21450co4 [1,0,0,-20973713,-36972739083] 2
21450cp (4 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+  0 11- 13- -2  4
Curve Equation t Generators 21450cp1 [1,0,0,137,-13783] 2 [38:197:1] 21450cp2 [1,0,0,-7863,-261783] 4 [-54:105:1] 21450cp3 [1,0,0,-18863,629217] 2 [-128:1039:1] 21450cp4 [1,0,0,-124863,-16992783] 2 [-204:105:1]
21450cq (4 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+  0 11- 13- -6  0
Curve Equation t Generators 21450cq1 [1,0,0,-43739213,40767414417] 2 [7362:339519:1] 21450cq2 [1,0,0,-568027213,5206577078417] 4 [3458:1810367:1] 21450cq3 [1,0,0,-438235213,7649132726417] 2 [6058:2280967:1] 21450cq4 [1,0,0,-9086427213,333377937078417] 2 [13842:14493279:1]
21450cr (2 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+ -2 11- 13- -2 -5
Curve Equation t Generators 21450cr1 [1,0,0,-4153,4550777] 5 [-172:515:1] 21450cr2 [1,0,0,-1612513,-896849983] 1 [202280:3280931:125]
21450cs (2 curves)	1	2- 3- 5+ 11- 13-	2- 3- 5+ -2 11- 13- -4 -2
Curve Equation t Generators 21450cs1 [1,0,0,1857187,-305122383] 2 [382:21259:1] 21450cs2 [1,0,0,-7822813,-2502482383] 2 [9182:-841141:1]
21450ct (1 curve)	1	2- 3- 5+ 11- 13-	2- 3- 5+ -5 11- 13-  4 -5
Curve Equation t Generators 21450ct1 [1,0,0,1287,-11583] 1 [72:639:1]
21450cu (1 curve)	1	2- 3- 5- 11+ 13-	2- 3- 5- -1 11+ 13-  2 -7
Curve Equation t Generators 21450cu1 [1,0,0,219427,-11209263] 1 [1222:-46241:1]
21450cv (1 curve)	1	2- 3- 5- 11- 13+	2- 3- 5-  1 11- 13+ -6  1
Curve Equation t Generators 21450cv1 [1,0,0,-248,2112] 1 [-8:64:1]
21450cw (1 curve)	1	2- 3- 5- 11- 13+	2- 3- 5- -3 11- 13+ -3  1
Curve Equation t Generators 21450cw1 [1,0,0,7703487,1925083017] 1 [3102:-237501:1]
21450cx (2 curves)	0	2- 3- 5- 11- 13-	2- 3- 5-  3 11- 13- -2  5
Curve Equation t 21450cx1 [1,0,0,-13012803,-18068847903] 1 21450cx2 [1,0,0,-9963328,-26749923328] 5

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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