Cremona's table of elliptic curves

84474 = 2 · 3² · 13 · 19²

Class	r	Atkin-Lehner	Eigenvalues
84474a (1 curve)	1	2+ 3+ 13+ 19+	2+ 3+  0  1  5 13+  6 19+
Curve Equation t Generators 84474a1 [1,-1,0,57873,-18817345] 1 [375617:5754203:1331]
84474b (1 curve)	1	2+ 3+ 13+ 19+	2+ 3+  3 -5 -4 13+ -6 19+
Curve Equation t Generators 84474b1 [1,-1,0,20984682,296760558068] 1 [18805804:13644067626:24389]
84474c (1 curve)	1	2+ 3+ 13+ 19+	2+ 3+ -4 -2  4 13+ -4 19+
Curve Equation t Generators 84474c1 [1,-1,0,-609,13859] 1 [43:235:1]
84474d (2 curves)	0	2+ 3+ 13+ 19-	2+ 3+  0  2  0 13+  0 19-
Curve Equation t 84474d1 [1,-1,0,303,2269] 1 84474d2 [1,-1,0,-8817,322685] 1
84474e (1 curve)	2	2+ 3+ 13- 19+	2+ 3+  0  1 -5 13- -6 19+
Curve Equation t Generators 84474e1 [1,-1,0,18,-106] 1 [5:7:1]&[25:112:1]
84474f (2 curves)	0	2+ 3+ 13- 19+	2+ 3+  0  2  0 13-  0 19+
Curve Equation t 84474f1 [1,-1,0,-353667,81502389] 3 84474f2 [1,-1,0,983838,433979540] 1
84474g (1 curve)	2	2+ 3+ 13- 19+	2+ 3+ -3 -5  4 13-  6 19+
Curve Equation t Generators 84474g1 [1,-1,0,6459,1600853] 1 [-71:919:1]&[154:2419:1]
84474h (2 curves)	1	2+ 3+ 13- 19-	2+ 3+  0  0 -6 13-  4 19-
Curve Equation t Generators 84474h1 [1,-1,0,-66672,-6424576] 2 [-155:487:1] 84474h2 [1,-1,0,19968,-22002448] 2 [1924:83512:1]
84474i (2 curves)	1	2+ 3+ 13- 19-	2+ 3+  2 -2  4 13-  0 19-
Curve Equation t Generators 84474i1 [1,-1,0,-10356,783872] 2 [356:6312:1] 84474i2 [1,-1,0,-205296,35834084] 2 [250:172:1]
84474j (1 curve)	1	2+ 3+ 13- 19-	2+ 3+  2  5 -3 13-  0 19-
Curve Equation t Generators 84474j1 [1,-1,0,-819202386,-24353128879020] 1 [354942677730237261:148497397261474577679:1963926099667]
84474k (1 curve)	1	2+ 3+ 13- 19-	2+ 3+ -2 -5  5 13-  4 19-
Curve Equation t Generators 84474k1 [1,-1,0,-128403,-17844811] 1 [1373:48229:1]
84474l (1 curve)	1	2+ 3+ 13- 19-	2+ 3+  4 -2 -4 13-  4 19-
Curve Equation t Generators 84474l1 [1,-1,0,-24435,3488123] 1 [-5245:265961:125]
84474m (1 curve)	0	2+ 3- 13+ 19+	2+ 3- -2 -5 -1 13+  0 19+
Curve Equation t 84474m1 [1,-1,0,2259612,-5958910256] 1
84474n (2 curves)	1	2+ 3- 13+ 19-	2+ 3-  0 -1 -3 13+ -6 19-
Curve Equation t Generators 84474n1 [1,-1,0,-505287,208877629] 1 [-603:17449:1] 84474n2 [1,-1,0,4124538,-3234415820] 1 [14670:812135:8]
84474o (4 curves)	1	2+ 3- 13+ 19-	2+ 3-  2  0  0 13+  6 19-
Curve Equation t Generators 84474o1 [1,-1,0,-479768526,-4043511471020] 2 [15743469032926295:3425863670068365488:275259237625] 84474o2 [1,-1,0,-546308046,-2849220242348] 4 [36022698958214977910089668778485:7791451802571985742193552711109904:627735734513917401455322875] 84474o3 [1,-1,0,1727472114,-20435090755820] 2 [595002522304780427:137090746446418873403:31312467371359] 84474o4 [1,-1,0,-3884720526,91170490431892] 2 [-1619584853484796:-669929295413625022:49552182217]
84474p (4 curves)	1	2+ 3- 13+ 19-	2+ 3- -2  4  4 13+ -2 19-
Curve Equation t Generators 84474p1 [1,-1,0,-63423,128365965] 2 [-814051630:-11034745065:1685159] 84474p2 [1,-1,0,-4222143,3309786765] 4 [-731262:17914119:343] 84474p3 [1,-1,0,-7601103,-2733821091] 2 [-164146777725:-3312553031166:70444997] 84474p4 [1,-1,0,-67382703,212914421181] 2 [1625190:-839973:343]
84474q (3 curves)	1	2+ 3- 13+ 19-	2+ 3-  3 -1 -6 13+  3 19-
Curve Equation t Generators 84474q1 [1,-1,0,1557,38407] 1 [1005:27836:125] 84474q2 [1,-1,0,-14688,-1361912] 1 [168926820:24461948551:8000] 84474q3 [1,-1,0,-1492983,-701778083] 1 [14364145928675131598171580:2077208625492588618285491569:679796025413392952000]
84474r (2 curves)	1	2+ 3- 13+ 19-	2+ 3- -3 -1  0 13+  6 19-
Curve Equation t Generators 84474r1 [1,-1,0,27549,-55279067] 1 [746:-19867:1] 84474r2 [1,-1,0,-10158066,-12460432172] 1 [33236:6013526:1]
84474s (1 curve)	1	2+ 3- 13- 19+	2+ 3-  2  0  3 13-  3 19+
Curve Equation t Generators 84474s1 [1,-1,0,-86166,17610804] 1 [-140:5258:1]
84474t (1 curve)	1	2+ 3- 13- 19+	2+ 3- -2 -1 -3 13-  4 19+
Curve Equation t Generators 84474t1 [1,-1,0,-21506823,38410678111] 1 [3159:43004:1]
84474u (1 curve)	2	2+ 3- 13- 19-	2+ 3-  0  0 -3 13- -2 19-
Curve Equation t Generators 84474u1 [1,-1,0,-5397,154079] 1 [-43:574:1]&[35:67:1]
84474v (1 curve)	2	2+ 3- 13- 19-	2+ 3-  0  0 -3 13- -7 19-
Curve Equation t Generators 84474v1 [1,-1,0,2321343,-592600131] 1 [306:11943:1]&[9990:516681:8]
84474w (1 curve)	0	2+ 3- 13- 19-	2+ 3-  0  0  4 13- -2 19-
Curve Equation t 84474w1 [1,-1,0,-144289782,-667192985996] 1
84474x (1 curve)	0	2+ 3- 13- 19-	2+ 3-  0  3 -5 13- -2 19-
Curve Equation t 84474x1 [1,-1,0,-1692,-686120] 1
84474y (1 curve)	2	2+ 3- 13- 19-	2+ 3-  0 -3  3 13-  2 19-
Curve Equation t Generators 84474y1 [1,-1,0,-42872247,130041216477] 1 [5781:-277431:1]&[81:355725:1]
84474z (1 curve)	0	2+ 3- 13- 19-	2+ 3- -1 -1  0 13-  3 19-
Curve Equation t 84474z1 [1,-1,0,40545,1421037] 1
84474ba (4 curves)	0	2+ 3- 13- 19-	2+ 3- -2  4 -4 13- -2 19-
Curve Equation t 84474ba1 [1,-1,0,12387,176309] 2 84474ba2 [1,-1,0,-52593,1488905] 4 84474ba3 [1,-1,0,-474963,-124799725] 2 84474ba4 [1,-1,0,-669903,211003919] 2
84474bb (1 curve)	0	2+ 3- 13- 19-	2+ 3-  3  3  0 13-  2 19-
Curve Equation t 84474bb1 [1,-1,0,38518452,209857771728] 1
84474bc (1 curve)	0	2+ 3- 13- 19-	2+ 3-  3  3  0 13- -5 19-
Curve Equation t 84474bc1 [1,-1,0,-198798,-34077898] 1
84474bd (1 curve)	0	2+ 3- 13- 19-	2+ 3-  4 -2  5 13- -2 19-
Curve Equation t 84474bd1 [1,-1,0,-780,-116272] 1
84474be (1 curve)	0	2+ 3- 13- 19-	2+ 3- -4  2 -3 13-  6 19-
Curve Equation t 84474be1 [1,-1,0,-335470689,2365077597309] 1
84474bf (1 curve)	0	2- 3+ 13+ 19+	2- 3+  0  1 -5 13+ -6 19+
Curve Equation t 84474bf1 [1,-1,1,6430,694795] 1
84474bg (1 curve)	0	2- 3+ 13+ 19+	2- 3+ -3 -5  4 13+  6 19+
Curve Equation t 84474bg1 [1,-1,1,2331631,-10991908991] 1
84474bh (1 curve)	0	2- 3+ 13+ 19+	2- 3+  4 -2 -4 13+  4 19+
Curve Equation t 84474bh1 [1,-1,1,-68,-491] 1
84474bi (2 curves)	1	2- 3+ 13+ 19-	2- 3+  0  2  0 13+  0 19-
Curve Equation t Generators 84474bi1 [1,-1,1,-980,-11625] 1 [41:105:1] 84474bi2 [1,-1,1,2725,-63989] 1 [139:1658:1]
84474bj (1 curve)	1	2- 3+ 13- 19+	2- 3+  0  1  5 13-  6 19+
Curve Equation t Generators 84474bj1 [1,-1,1,160,2701] 1 [-74:185:8]
84474bk (2 curves)	1	2- 3+ 13- 19+	2- 3+  0  2  0 13-  0 19+
Curve Equation t Generators 84474bk1 [1,-1,1,109315,-16109755] 3 [1758:33515:8] 84474bk2 [1,-1,1,-3183005,-2197381499] 1 [21662:749431:8]
84474bl (1 curve)	1	2- 3+ 13- 19+	2- 3+  3 -5 -4 13- -6 19+
Curve Equation t Generators 84474bl1 [1,-1,1,58129,-43281161] 1 [1411:52646:1]
84474bm (2 curves)	0	2- 3+ 13- 19-	2- 3+  0  0  6 13- -4 19-
Curve Equation t 84474bm1 [1,-1,1,-600050,174063601] 2 84474bm2 [1,-1,1,179710,593886385] 2
84474bn (1 curve)	2	2- 3+ 13- 19-	2- 3+  2 -5 -5 13- -4 19-
Curve Equation t Generators 84474bn1 [1,-1,1,-1155629,482965525] 1 [575:-3176:1]&[385:9554:1]
84474bo (2 curves)	0	2- 3+ 13- 19-	2- 3+ -2 -2 -4 13-  0 19-
Curve Equation t 84474bo1 [1,-1,1,-1151,-28649] 2 84474bo2 [1,-1,1,-22811,-1319585] 2
84474bp (1 curve)	0	2- 3+ 13- 19-	2- 3+ -2  5  3 13-  0 19-
Curve Equation t 84474bp1 [1,-1,1,-7372821476,657541852555015] 1
84474bq (1 curve)	0	2- 3+ 13- 19-	2- 3+ -4 -2  4 13- -4 19-
Curve Equation t 84474bq1 [1,-1,1,-219917,-93959405] 1
84474br (1 curve)	1	2- 3- 13+ 19+	2- 3-  0  0 -3 13+ -2 19+
Curve Equation t Generators 84474br1 [1,-1,1,-1948385,-1047086045] 1 [11146897965202634:2381997794666816207:242737073272]
84474bs (1 curve)	1	2- 3- 13+ 19+	2- 3-  0  0 -3 13+ -7 19+
Curve Equation t Generators 84474bs1 [1,-1,1,6430,84705] 1 [5:339:1]
84474bt (1 curve)	1	2- 3- 13+ 19+	2- 3-  0  0  4 13+ -2 19+
Curve Equation t Generators 84474bt1 [1,-1,1,-399695,97377815] 1 [351:-662:1]
84474bu (1 curve)	1	2- 3- 13+ 19+	2- 3- -2 -1 -3 13+  4 19+
Curve Equation t Generators 84474bu1 [1,-1,1,-59576,-5584363] 1 [2430:15323:8]
84474bv (1 curve)	1	2- 3- 13+ 19+	2- 3-  4 -2  5 13+ -2 19+
Curve Equation t Generators 84474bv1 [1,-1,1,-281648,798917779] 1 [-451:29105:1]
84474bw (1 curve)	1	2- 3- 13+ 19+	2- 3- -4  2 -3 13+  6 19+
Curve Equation t Generators 84474bw1 [1,-1,1,-929282,-344569215] 1 [4281:270111:1]
84474bx (1 curve)	0	2- 3- 13+ 19-	2- 3-  1 -3 -2 13+  0 19-
Curve Equation t 84474bx1 [1,-1,1,-19562,-18942883] 1
84474by (1 curve)	0	2- 3- 13+ 19-	2- 3-  1 -3  4 13+  3 19-
Curve Equation t 84474by1 [1,-1,1,-3252317,2369851877] 1
84474bz (1 curve)	0	2- 3- 13+ 19-	2- 3-  2  0  3 13+  3 19-
Curve Equation t 84474bz1 [1,-1,1,-239,-2505] 1
84474ca (6 curves)	0	2- 3- 13+ 19-	2- 3-  2  0 -4 13+ -2 19-
Curve Equation t 84474ca1 [1,-1,1,-126779,108971691] 2 84474ca2 [1,-1,1,-4285499,3401014443] 4 84474ca3 [1,-1,1,-6624779,-720796917] 4 84474ca4 [1,-1,1,-68485739,218163657291] 2 84474ca5 [1,-1,1,26320081,-5767949469] 2 84474ca6 [1,-1,1,-76998119,-259497642765] 2
84474cb (3 curves)	0	2- 3- 13+ 19-	2- 3-  3 -1  6 13+  0 19-
Curve Equation t 84474cb1 [1,-1,1,42067984,77899622739] 1 84474cb2 [1,-1,1,-435145136,-4709996453037] 1 84474cb3 [1,-1,1,-38552348156,-2913553164259821] 1
84474cc (1 curve)	0	2- 3- 13+ 19-	2- 3- -4 -3 -1 13+ -2 19-
Curve Equation t 84474cc1 [1,-1,1,-246992,-47285715] 1
84474cd (1 curve)	2	2- 3- 13- 19+	2- 3- -2 -5 -1 13-  0 19+
Curve Equation t Generators 84474cd1 [1,-1,1,6259,867125] 1 [-71:282:1]&[33:-1070:1]
84474ce (2 curves)	1	2- 3- 13- 19-	2- 3-  1  1  2 13-  3 19-
Curve Equation t Generators 84474ce1 [1,-1,1,-8732,482527] 1 [-109:415:1] 84474ce2 [1,-1,1,-691022,-242412713] 1 [29739500:778583917:21952]
84474cf (1 curve)	1	2- 3- 13- 19-	2- 3-  1 -1  2 13-  0 19-
Curve Equation t Generators 84474cf1 [1,-1,1,61663,5034737] 1 [81:-3290:1]
84474cg (1 curve)	1	2- 3- 13- 19-	2- 3-  3 -3 -2 13-  4 19-
Curve Equation t Generators 84474cg1 [1,-1,1,-656366,211438653] 1 [3197:173847:1]

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