Cremona's table of elliptic curves

27225 = 3² · 5² · 11²

Class	r	Atkin-Lehner	Eigenvalues
27225a (2 curves)	0	3+ 5+ 11-	0 3+ 5+  5 11-  2  0  7
Curve Equation t 27225a1 [0,0,1,0,-5032844] 1 27225a2 [0,0,1,0,135886781] 1
27225b (2 curves)	0	3+ 5+ 11-	0 3+ 5+  5 11-  5  0  1
Curve Equation t 27225b1 [0,0,1,0,-1664] 1 27225b2 [0,0,1,0,44921] 1
27225c (2 curves)	0	3+ 5+ 11-	0 3+ 5+  5 11- -7  0 -8
Curve Equation t 27225c1 [0,0,1,0,-8594] 1 27225c2 [0,0,1,0,232031] 1
27225d (2 curves)	2	3+ 5+ 11-	0 3+ 5+ -5 11- -2  0 -7
Curve Equation t Generators 27225d1 [0,0,1,0,3781] 1 [-110:271:8]&[-11:49:1] 27225d2 [0,0,1,0,-102094] 1 [60:337:1]&[530:3471:8]
27225e (2 curves)	0	3+ 5+ 11-	0 3+ 5+ -5 11-  7  0  8
Curve Equation t 27225e1 [0,0,1,0,11438281] 1 27225e2 [0,0,1,0,-308833594] 1
27225f (1 curve)	0	3+ 5+ 11-	1 3+ 5+  0 11-  5  6  1
Curve Equation t 27225f1 [1,-1,0,-8817,320876] 1
27225g (1 curve)	0	3+ 5+ 11-	1 3+ 5+  0 11- -5  6 -1
Curve Equation t 27225g1 [1,-1,0,-118542,15738971] 1
27225h (2 curves)	0	3+ 5+ 11-	1 3+ 5+ -2 11- -2 -2  6
Curve Equation t 27225h1 [1,-1,0,-45942,-690409] 2 27225h2 [1,-1,0,-454317,117329966] 2
27225i (1 curve)	0	3+ 5+ 11-	1 3+ 5+ -3 11-  2  3  1
Curve Equation t 27225i1 [1,-1,0,-127617,94787666] 1
27225j (1 curve)	0	3+ 5+ 11-	-1 3+ 5+  0 11-  5 -6  1
Curve Equation t 27225j1 [1,-1,1,-980,-11558] 1
27225k (1 curve)	0	3+ 5+ 11-	-1 3+ 5+  0 11- -5 -6 -1
Curve Equation t 27225k1 [1,-1,1,-1066880,-423885338] 1
27225l (2 curves)	0	3+ 5+ 11-	-1 3+ 5+ -2 11- -2  2  6
Curve Equation t 27225l1 [1,-1,1,-5105,27272] 2 27225l2 [1,-1,1,-50480,-4328728] 2
27225m (1 curve)	0	3+ 5+ 11-	-1 3+ 5+ -3 11-  2 -3  1
Curve Equation t 27225m1 [1,-1,1,-14180,-3505928] 1
27225n (1 curve)	0	3+ 5+ 11-	2 3+ 5+  3 11-  2  6 -5
Curve Equation t 27225n1 [0,0,1,-825,9281] 1
27225o (1 curve)	0	3+ 5+ 11-	2 3+ 5+ -3 11- -2  6  5
Curve Equation t 27225o1 [0,0,1,-898425,333540281] 1
27225p (1 curve)	0	3+ 5+ 11-	-2 3+ 5+  3 11-  2 -6 -5
Curve Equation t 27225p1 [0,0,1,-7425,-250594] 1
27225q (1 curve)	0	3+ 5+ 11-	-2 3+ 5+ -3 11- -2 -6  5
Curve Equation t 27225q1 [0,0,1,-99825,-12353344] 1
27225r (2 curves)	1	3+ 5- 11-	0 3+ 5-  5 11- -7  0  8
Curve Equation t Generators 27225r1 [0,0,1,0,91506] 3 [-350:701:8] 27225r2 [0,0,1,0,-2470669] 1 [50585430:294296143:343000]
27225s (2 curves)	1	3+ 5- 11-	0 3+ 5- -5 11- -5  0  1
Curve Equation t Generators 27225s1 [0,0,1,0,-207969] 1 [275:4537:1] 27225s2 [0,0,1,0,5615156] 1 [264:4900:1]
27225t (2 curves)	1	3+ 5- 11-	0 3+ 5- -5 11-  7  0 -8
Curve Equation t Generators 27225t1 [0,0,1,0,-69] 1 [5:7:1] 27225t2 [0,0,1,0,1856] 1 [-6:40:1]
27225u (1 curve)	1	3+ 5- 11-	1 3+ 5-  0 11-  5  6 -1
Curve Equation t Generators 27225u1 [1,-1,0,-26671992,-53012339209] 1 [86432941391298976704418:-15906540578779868539488731:2505099538368162091]
27225v (1 curve)	1	3+ 5- 11-	1 3+ 5-  0 11- -5  6  1
Curve Equation t Generators 27225v1 [1,-1,0,-24492,-1469209] 1 [238:2359:1]
27225w (1 curve)	1	3+ 5- 11-	1 3+ 5-  3 11- -2  3  1
Curve Equation t Generators 27225w1 [1,-1,0,-567,-27934] 1 [58:-392:1]
27225x (1 curve)	1	3+ 5- 11-	-1 3+ 5-  0 11-  5 -6 -1
Curve Equation t Generators 27225x1 [1,-1,1,-2963555,1964407822] 1 [994:-535:1]
27225y (1 curve)	1	3+ 5- 11-	-1 3+ 5-  0 11- -5 -6  1
Curve Equation t Generators 27225y1 [1,-1,1,-220430,39889072] 1 [268:-40:1]
27225z (1 curve)	1	3+ 5- 11-	-1 3+ 5-  3 11- -2 -3  1
Curve Equation t Generators 27225z1 [1,-1,1,-5105,759322] 1 [223:3155:1]
27225ba (2 curves)	0	3- 5+ 11+	0 3- 5+  0 11+  0  0  0
Curve Equation t 27225ba1 [0,0,1,-1650,-26469] 1 27225ba2 [0,0,1,-199650,35229906] 1
27225bb (1 curve)	0	3- 5+ 11+	1 3- 5+  1 11+ -2 -3 -3
Curve Equation t 27225bb1 [1,-1,0,-158472,28450021] 1
27225bc (2 curves)	0	3- 5+ 11+	1 3- 5+ -2 11+  4  6  6
Curve Equation t 27225bc1 [1,-1,0,-3042,39991] 2 27225bc2 [1,-1,0,9333,275116] 2
27225bd (1 curve)	0	3- 5+ 11+	-1 3- 5+ -1 11+  2  3  3
Curve Equation t 27225bd1 [1,-1,1,-1310,-21018] 1
27225be (2 curves)	0	3- 5+ 11+	-1 3- 5+  2 11+ -4 -6 -6
Curve Equation t 27225be1 [1,-1,1,-368105,-52123728] 2 27225be2 [1,-1,1,1129270,-369567228] 2
27225bf (2 curves)	1	3- 5+ 11-	0 3- 5+  1 11- -2  6 -7
Curve Equation t Generators 27225bf1 [0,0,1,-1397550,1784829406] 1 [334:36814:1] 27225bf2 [0,0,1,-163114050,801836784031] 1 [7381:1633:1]
27225bg (2 curves)	1	3- 5+ 11-	0 3- 5+ -1 11- -1  6  7
Curve Equation t Generators 27225bg1 [0,0,1,-25410,1635466] 1 [-44:1633:1] 27225bg2 [0,0,1,137940,2893261] 1 [451:12523:1]
27225bh (2 curves)	1	3- 5+ 11-	0 3- 5+ -1 11-  2 -6  7
Curve Equation t Generators 27225bh1 [0,0,1,-11550,-1340969] 1 [301:4738:1] 27225bh2 [0,0,1,-1348050,-602431844] 1 [7726:670936:1]
27225bi (8 curves)	1	3- 5+ 11-	1 3- 5+  0 11- -2 -2 -4
Curve Equation t Generators 27225bi1 [1,-1,0,-567,837216] 2 [-36:918:1] 27225bi2 [1,-1,0,-136692,19214091] 4 [58:3359:1] 27225bi3 [1,-1,0,-272817,-25298784] 4 [-6188:29351:64] 27225bi4 [1,-1,0,-2178567,1238213466] 2 [234:27108:1] 27225bi5 [1,-1,0,952308,-190690659] 2 [16000763646:137799899427:81746504] 27225bi6 [1,-1,0,-3675942,-2710364409] 4 [30650457966:240010967517:13651919] 27225bi7 [1,-1,0,-2995317,-3745595034] 2 [57375236203235348:-521489875681034921:26029076411456] 27225bi8 [1,-1,0,-58806567,-173560171284] 2 [-85184963190607628948:42538985788715314121:19241076049937344]
27225bj (2 curves)	1	3- 5+ 11-	1 3- 5+  2 11- -1 -5  6
Curve Equation t Generators 27225bj1 [1,-1,0,-567,20466] 1 [-30:114:1] 27225bj2 [1,-1,0,-817317,-284208534] 1 [1905711690:-755151509328:12167]
27225bk (1 curve)	1	3- 5+ 11-	1 3- 5+ -3 11-  4  0 -4
Curve Equation t Generators 27225bk1 [1,-1,0,-318192,149863841] 1 [-36175048:196925049:50653]
27225bl (4 curves)	1	3- 5+ 11-	-1 3- 5+  0 11-  2 -6  4
Curve Equation t Generators 27225bl1 [1,-1,1,22120,977122] 2 [8:1070:1] 27225bl2 [1,-1,1,-114005,8872372] 4 [-250:4783:1] 27225bl3 [1,-1,1,-794630,-266100128] 2 [2179:90260:1] 27225bl4 [1,-1,1,-1611380,787507372] 2 [-976:38300:1]
27225bm (2 curves)	1	3- 5+ 11-	-1 3- 5+ -2 11-  1  5 -6
Curve Equation t Generators 27225bm1 [1,-1,1,-6755,215372] 1 [48:-20:1] 27225bm2 [1,-1,1,-68630,-27034378] 1 [5327766:60237410:12167]
27225bn (1 curve)	1	3- 5+ 11-	-1 3- 5+  3 11- -4  0  4
Curve Equation t Generators 27225bn1 [1,-1,1,-2630,-111878] 1 [1304:46385:1]
27225bo (4 curves)	1	3- 5+ 11-	-1 3- 5+  4 11- -2  2  0
Curve Equation t Generators 27225bo1 [1,-1,1,-177530,-28504528] 2 [-1677548:4196664:6859] 27225bo2 [1,-1,1,-313655,21317222] 4 [-470:8281:1] 27225bo3 [1,-1,1,1183720,165065222] 2 [1884:94345:1] 27225bo4 [1,-1,1,-3989030,3064527722] 2 [-1812:66790:1]
27225bp (1 curve)	1	3- 5+ 11-	2 3- 5+  1 11- -2 -4  3
Curve Equation t Generators 27225bp1 [0,0,1,825,-1719] 1 [450:3771:8]
27225bq (3 curves)	1	3- 5+ 11-	2 3- 5+ -2 11-  4  2  0
Curve Equation t Generators 27225bq1 [0,0,1,-9075,790281] 1 [7458:226629:8] 27225bq2 [0,0,1,-281325,-104025969] 1 [9990552730365396618:-250581881567115675377:9894341542822568] 27225bq3 [0,0,1,-212908575,-1195742989719] 1 [29792225981428486770851890010693601091571641034424121955340086378977198343968243952202:-3476902246672162887646989980321583583435290321537606897196434425293393583331846994350999:1222497782825593106002385572325540628661153316538582041494829024344205654414173352]
27225br (1 curve)	1	3- 5+ 11-	-2 3- 5+ -1 11-  2  4 -3
Curve Equation t Generators 27225br1 [0,0,1,99825,2287656] 1 [0:1512:1]
27225bs (2 curves)	1	3- 5+ 11-	-2 3- 5+ -3 11-  1 -2  5
Curve Equation t Generators 27225bs1 [0,0,1,1815,131436] 1 [44:544:1] 27225bs2 [0,0,1,-226875,-42633594] 1 [13618:536873:8]
27225bt (1 curve)	1	3- 5- 11+	1 3- 5-  1 11+ -2 -3  3
Curve Equation t Generators 27225bt1 [1,-1,0,-32742,-2659959] 1 [16692:154707:64]
27225bu (2 curves)	1	3- 5- 11+	1 3- 5- -4 11+ -2  2  8
Curve Equation t Generators 27225bu1 [1,-1,0,-218367,267424416] 2 [-24903120:344983532:35937] 27225bu2 [1,-1,0,-7705242,8196025041] 2 [2264064:2847093:1331]
27225bv (2 curves)	1	3- 5- 11+	1 3- 5- -4 11+ -2  2 -8
Curve Equation t Generators 27225bv1 [1,-1,0,-72,-1589] 2 [18:43:1] 27225bv2 [1,-1,0,-2547,-48614] 2 [-30:26:1]
27225bw (1 curve)	1	3- 5- 11+	-1 3- 5- -1 11+  2  3 -3
Curve Equation t Generators 27225bw1 [1,-1,1,-3961805,3552290822] 1 [-8226:650975:8]
27225bx (2 curves)	1	3- 5- 11+	-1 3- 5-  4 11+  2 -2  8
Curve Equation t Generators 27225bx1 [1,-1,1,-8735,2141142] 2 [18:1401:1] 27225bx2 [1,-1,1,-308210,65629842] 2 [-30:8666:1]
27225by (2 curves)	1	3- 5- 11+	-1 3- 5-  4 11+  2 -2 -8
Curve Equation t Generators 27225by1 [1,-1,1,-1805,-200428] 2 [598:14271:1] 27225by2 [1,-1,1,-63680,-6140428] 2 [-140:196:1]
27225bz (2 curves)	0	3- 5- 11-	0 3- 5-  1 11-  1 -6  7
Curve Equation t 27225bz1 [0,0,1,-635250,204433281] 1 27225bz2 [0,0,1,3448500,361657656] 1
27225ca (2 curves)	0	3- 5- 11-	2 3- 5-  3 11- -1  2  5
Curve Equation t 27225ca1 [0,0,1,-9075,-341069] 1 27225ca2 [0,0,1,45375,16429531] 1

Data from Elliptic Curve Data by J. E. Cremona.
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