Cremona's table of elliptic curves

20286 = 2 · 3² · 7² · 23

Class	r	Atkin-Lehner	Eigenvalues
20286a (1 curve)	1	2+ 3+ 7+ 23+	2+ 3+ -1 7+  0  5 -7 -8
Curve Equation t Generators 20286a1 [1,-1,0,-1920,-32768] 1 [128:1280:1]
20286b (1 curve)	1	2+ 3+ 7+ 23+	2+ 3+  2 7+ -1  2  3  0
Curve Equation t Generators 20286b1 [1,-1,0,4989,310869] 1 [195:2847:1]
20286c (1 curve)	1	2+ 3+ 7+ 23+	2+ 3+  2 7+  3  2 -1 -8
Curve Equation t Generators 20286c1 [1,-1,0,31449,165535] 1 [233:4367:1]
20286d (1 curve)	1	2+ 3+ 7+ 23+	2+ 3+ -3 7+  4 -3  3  0
Curve Equation t Generators 20286d1 [1,-1,0,-101129541,-391414687147] 1 [143327938:-36216214481:2197]
20286e (1 curve)	0	2+ 3+ 7- 23+	2+ 3+  1 7-  0 -5  7  8
Curve Equation t 20286e1 [1,-1,0,-94089,11427597] 1
20286f (1 curve)	0	2+ 3+ 7- 23+	2+ 3+  1 7-  2  1 -6  6
Curve Equation t 20286f1 [1,-1,0,-744,-7778] 1
20286g (1 curve)	0	2+ 3+ 7- 23+	2+ 3+ -2 7- -1 -2 -3  0
Curve Equation t 20286g1 [1,-1,0,244452,-107116976] 1
20286h (1 curve)	0	2+ 3+ 7- 23+	2+ 3+ -2 7-  3 -2  1  8
Curve Equation t 20286h1 [1,-1,0,642,-666] 1
20286i (1 curve)	0	2+ 3+ 7- 23+	2+ 3+  3 7-  4  3 -3  0
Curve Equation t 20286i1 [1,-1,0,-2063868,1141740368] 1
20286j (2 curves)	0	2+ 3+ 7- 23+	2+ 3+  3 7-  6 -5  6 -2
Curve Equation t 20286j1 [1,-1,0,-547143,-155638883] 1 20286j2 [1,-1,0,-500838,-183100492] 1
20286k (1 curve)	1	2+ 3+ 7- 23-	2+ 3+  1 7-  0  3  2 -4
Curve Equation t Generators 20286k1 [1,-1,0,4603296,2871489536] 1 [-27643905:3480209279:91125]
20286l (1 curve)	1	2+ 3+ 7- 23-	2+ 3+ -1 7-  0 -3 -2  4
Curve Equation t Generators 20286l1 [1,-1,0,93945,-8398531] 1 [109:1714:1]
20286m (1 curve)	1	2+ 3+ 7- 23-	2+ 3+ -1 7-  2  5  2  2
Curve Equation t Generators 20286m1 [1,-1,0,16455,-2184211] 1 [149:1812:1]
20286n (1 curve)	0	2+ 3- 7+ 23+	2+ 3-  0 7+ -1 -6 -5  6
Curve Equation t 20286n1 [1,-1,0,-18972,-1003752] 1
20286o (1 curve)	0	2+ 3- 7+ 23+	2+ 3- -1 7+  3  2  2 -2
Curve Equation t 20286o1 [1,-1,0,-46755,-33949931] 1
20286p (1 curve)	0	2+ 3- 7+ 23+	2+ 3- -4 7+  5  2 -3  6
Curve Equation t 20286p1 [1,-1,0,-9,-2241] 1
20286q (1 curve)	1	2+ 3- 7+ 23-	2+ 3-  3 7+ -1 -6  2 -2
Curve Equation t Generators 20286q1 [1,-1,0,-1773,101443] 1 [41:290:1]
20286r (1 curve)	1	2+ 3- 7- 23+	2+ 3-  0 7- -1  6  5 -6
Curve Equation t Generators 20286r1 [1,-1,0,-387,3037] 1 [11:-1:1]
20286s (2 curves)	1	2+ 3- 7- 23+	2+ 3-  0 7-  4  2  2  6
Curve Equation t Generators 20286s1 [1,-1,0,-188757,31938997] 2 [234:619:1] 20286s2 [1,-1,0,-3028797,2029623133] 2 [8046:-3737:8]
20286t (2 curves)	1	2+ 3- 7- 23+	2+ 3-  0 7-  4 -2 -2 -6
Curve Equation t Generators 20286t1 [1,-1,0,-3852,-92016] 2 [135:1287:1] 20286t2 [1,-1,0,-61812,-5899608] 2 [319:2442:1]
20286u (1 curve)	1	2+ 3- 7- 23+	2+ 3-  1 7-  0  1  4 -4
Curve Equation t Generators 20286u1 [1,-1,0,-271224,-54484704] 1 [1171:34523:1]
20286v (1 curve)	1	2+ 3- 7- 23+	2+ 3-  1 7-  3 -2 -2  2
Curve Equation t Generators 20286v1 [1,-1,0,-954,99252] 1 [3:309:1]
20286w (2 curves)	1	2+ 3- 7- 23+	2+ 3- -2 7-  2  4 -6  0
Curve Equation t Generators 20286w1 [1,-1,0,-6183,49405] 2 [-33:482:1] 20286w2 [1,-1,0,-76743,8192029] 2 [-117:4003:1]
20286x (4 curves)	1	2+ 3- 7- 23+	2+ 3- -2 7- -4 -2  6  0
Curve Equation t Generators 20286x1 [1,-1,0,-264168,-85182224] 2 [695:7811:1] 20286x2 [1,-1,0,-4929948,-4210664900] 4 [15507:1902242:1] 20286x3 [1,-1,0,-78872418,-269590189730] 2 [-89079656323:44453665514:17373979] 20286x4 [1,-1,0,-5639958,-2918020694] 2 [5321799:652138220:343]
20286y (2 curves)	1	2+ 3- 7- 23+	2+ 3- -2 7- -6  4 -2 -4
Curve Equation t Generators 20286y1 [1,-1,0,-1773,26865] 2 [-33:237:1] 20286y2 [1,-1,0,-6183,-155709] 2 [-47:195:1]
20286z (1 curve)	1	2+ 3- 7- 23+	2+ 3-  3 7- -2 -5  4  6
Curve Equation t Generators 20286z1 [1,-1,0,104382,22930452] 1 [247:7860:1]
20286ba (1 curve)	1	2+ 3- 7- 23+	2+ 3-  3 7- -4  3 -4  0
Curve Equation t Generators 20286ba1 [1,-1,0,4011327,2074146493] 1 [641:69740:1]
20286bb (1 curve)	1	2+ 3- 7- 23+	2+ 3- -3 7- -2  5 -4 -6
Curve Equation t Generators 20286bb1 [1,-1,0,5114709,-7875374459] 1 [34990:2488807:8]
20286bc (1 curve)	1	2+ 3- 7- 23+	2+ 3-  4 7-  5 -2  3 -6
Curve Equation t Generators 20286bc1 [1,-1,0,-450,769558] 1 [-1:878:1]
20286bd (4 curves)	0	2+ 3- 7- 23-	2+ 3-  2 7-  0  2  2  8
Curve Equation t 20286bd1 [1,-1,0,1314,17604] 2 20286bd2 [1,-1,0,-7506,171072] 4 20286bd3 [1,-1,0,-47196,-3805866] 2 20286bd4 [1,-1,0,-108936,13864122] 2
20286be (6 curves)	0	2+ 3- 7- 23-	2+ 3- -2 7-  4  2 -6 -4
Curve Equation t 20286be1 [1,-1,0,55557,10309221] 2 20286be2 [1,-1,0,-508923,119705445] 4 20286be3 [1,-1,0,-2237643,-1171648395] 4 20286be4 [1,-1,0,-7811883,8405643861] 2 20286be5 [1,-1,0,-34898103,-79341193359] 2 20286be6 [1,-1,0,2763297,-5669493831] 2
20286bf (2 curves)	2	2+ 3- 7- 23-	2+ 3- -3 7-  0 -5  0 -8
Curve Equation t Generators 20286bf1 [1,-1,0,1314,80716] 1 [-33:41:1]&[11:305:1] 20286bf2 [1,-1,0,-11916,-2282162] 1 [191:1448:1]&[317:4913:1]
20286bg (1 curve)	0	2+ 3- 7- 23-	2+ 3- -3 7- -1  6 -2  2
Curve Equation t 20286bg1 [1,-1,0,-86886,-34621182] 1
20286bh (1 curve)	1	2- 3+ 7+ 23-	2- 3+  1 7+  0  5  7 -8
Curve Equation t Generators 20286bh1 [1,-1,1,-17282,902017] 1 [121:-817:1]
20286bi (1 curve)	1	2- 3+ 7+ 23-	2- 3+ -2 7+  1  2 -3  0
Curve Equation t Generators 20286bi1 [1,-1,1,44899,-8438363] 1 [559:13544:1]
20286bj (1 curve)	1	2- 3+ 7+ 23-	2- 3+ -2 7+ -3  2  1 -8
Curve Equation t Generators 20286bj1 [1,-1,1,283039,-4752485] 1 [20596:689537:64]
20286bk (1 curve)	1	2- 3+ 7+ 23-	2- 3+  3 7+ -4 -3 -3  0
Curve Equation t Generators 20286bk1 [1,-1,1,-11236616,14500585803] 1 [1997:3705:1]
20286bl (1 curve)	1	2- 3+ 7- 23+	2- 3+  1 7-  0 -3  2  4
Curve Equation t Generators 20286bl1 [1,-1,1,10438,307577] 1 [-15:391:1]
20286bm (1 curve)	1	2- 3+ 7- 23+	2- 3+  1 7- -2  5 -2  2
Curve Equation t Generators 20286bm1 [1,-1,1,1828,80287] 1 [65:653:1]
20286bn (1 curve)	1	2- 3+ 7- 23+	2- 3+ -1 7-  0  3 -2 -4
Curve Equation t Generators 20286bn1 [1,-1,1,511477,-106521957] 1 [1899:86858:1]
20286bo (1 curve)	0	2- 3+ 7- 23-	2- 3+ -1 7-  0 -5 -7  8
Curve Equation t 20286bo1 [1,-1,1,-846803,-307698317] 1
20286bp (1 curve)	0	2- 3+ 7- 23-	2- 3+ -1 7- -2  1  6  6
Curve Equation t 20286bp1 [1,-1,1,-6698,216703] 1
20286bq (1 curve)	0	2- 3+ 7- 23-	2- 3+  2 7-  1 -2  3  0
Curve Equation t 20286bq1 [1,-1,1,2200066,2889958285] 1
20286br (1 curve)	0	2- 3+ 7- 23-	2- 3+  2 7- -3 -2 -1  8
Curve Equation t 20286br1 [1,-1,1,5776,12205] 1
20286bs (1 curve)	0	2- 3+ 7- 23-	2- 3+ -3 7- -4  3  3  0
Curve Equation t 20286bs1 [1,-1,1,-229319,-42210241] 1
20286bt (2 curves)	2	2- 3+ 7- 23-	2- 3+ -3 7- -6 -5 -6 -2
Curve Equation t Generators 20286bt1 [1,-1,1,-55649,6800049] 1 [-201:3236:1]&[-103:3432:1] 20286bt2 [1,-1,1,-4924289,4207174129] 1 [443:45740:1]&[1129:8696:1]
20286bu (1 curve)	1	2- 3- 7+ 23+	2- 3- -3 7+  5  0  4  0
Curve Equation t Generators 20286bu1 [1,-1,1,28876,7852079] 1 [207:4657:1]
20286bv (2 curves)	0	2- 3- 7+ 23-	2- 3-  0 7+  3  2  3  2
Curve Equation t 20286bv1 [1,-1,1,-42125,-12318379] 1 20286bv2 [1,-1,1,374620,311242439] 3
20286bw (1 curve)	0	2- 3- 7+ 23-	2- 3-  3 7+  2  3  3  0
Curve Equation t 20286bw1 [1,-1,1,-5081,-339447] 1
20286bx (2 curves)	0	2- 3- 7- 23+	2- 3-  0 7-  2  6  2  6
Curve Equation t 20286bx1 [1,-1,1,-230,1077045] 2 20286bx2 [1,-1,1,-158990,24065493] 2
20286by (4 curves)	0	2- 3- 7- 23+	2- 3-  0 7- -6 -2 -6 -2
Curve Equation t 20286by1 [1,-1,1,2048215,7945492713] 2 20286by2 [1,-1,1,-49390025,127302784809] 2 20286by3 [1,-1,1,-18491360,-218306963325] 2 20286by4 [1,-1,1,-668772320,-6624354756477] 2
20286bz (2 curves)	0	2- 3- 7- 23+	2- 3-  2 7-  0  0 -2 -4
Curve Equation t 20286bz1 [1,-1,1,-94604,11249151] 2 20286bz2 [1,-1,1,-1514624,717851103] 2
20286ca (2 curves)	0	2- 3- 7- 23+	2- 3-  2 7- -2 -2  6  4
Curve Equation t 20286ca1 [1,-1,1,-7040354,-7188418947] 2 20286ca2 [1,-1,1,-7009484,-7254604227] 2
20286cb (2 curves)	0	2- 3- 7- 23+	2- 3-  2 7-  4  4 -4  2
Curve Equation t 20286cb1 [1,-1,1,-6502334,7809310541] 2 20286cb2 [1,-1,1,-110366654,446282923853] 2
20286cc (2 curves)	0	2- 3- 7- 23+	2- 3-  2 7-  6  6 -2 -4
Curve Equation t 20286cc1 [1,-1,1,-19319,-948657] 2 20286cc2 [1,-1,1,21001,-4416177] 2
20286cd (2 curves)	0	2- 3- 7- 23+	2- 3- -2 7-  0  0  2  4
Curve Equation t 20286cd1 [1,-1,1,-1931,-32245] 2 20286cd2 [1,-1,1,-30911,-2084029] 2
20286ce (2 curves)	0	2- 3- 7- 23+	2- 3- -2 7- -2  2 -6 -4
Curve Equation t 20286ce1 [1,-1,1,-143681,20998541] 2 20286ce2 [1,-1,1,-143051,21191321] 2
20286cf (2 curves)	0	2- 3- 7- 23+	2- 3- -2 7-  4 -4 -8  2
Curve Equation t 20286cf1 [1,-1,1,-3611,389575] 2 20286cf2 [1,-1,1,-105041,13088611] 2
20286cg (2 curves)	0	2- 3- 7- 23+	2- 3- -2 7-  6 -6  2  4
Curve Equation t 20286cg1 [1,-1,1,-946616,327282491] 2 20286cg2 [1,-1,1,1029064,1512690491] 2
20286ch (1 curve)	0	2- 3- 7- 23+	2- 3-  3 7- -2  7  4  6
Curve Equation t 20286ch1 [1,-1,1,-35951,-3038857] 1
20286ci (1 curve)	0	2- 3- 7- 23+	2- 3-  3 7-  5  0 -4  0
Curve Equation t 20286ci1 [1,-1,1,589,-23061] 1
20286cj (1 curve)	2	2- 3- 7- 23+	2- 3- -3 7- -2 -7 -4 -6
Curve Equation t Generators 20286cj1 [1,-1,1,-734,9069] 1 [-19:135:1]&[-1:99:1]
20286ck (2 curves)	0	2- 3- 7- 23+	2- 3-  4 7- -2  2 -2  2
Curve Equation t 20286ck1 [1,-1,1,-4493,-133451] 2 20286ck2 [1,-1,1,-75053,-7895051] 2
20286cl (2 curves)	0	2- 3- 7- 23+	2- 3- -4 7- -2 -2  2  2
Curve Equation t 20286cl1 [1,-1,1,7708,-70045] 2 20286cl2 [1,-1,1,-31982,-546325] 2
20286cm (4 curves)	1	2- 3- 7- 23-	2- 3-  0 7-  0 -2  0 -2
Curve Equation t Generators 20286cm1 [1,-1,1,-15665,793041] 2 [17:720:1] 20286cm2 [1,-1,1,-253805,49278345] 2 [311:438:1] 20286cm3 [1,-1,1,83560,1594779] 2 [53:2457:1] 20286cm4 [1,-1,1,-339800,13110171] 2 [-243:9137:1]
20286cn (2 curves)	1	2- 3- 7- 23-	2- 3-  0 7-  3 -2 -3 -2
Curve Equation t Generators 20286cn1 [1,-1,1,-860,36159] 1 [83:687:1] 20286cn2 [1,-1,1,7645,-909597] 1 [731:19506:1]
20286co (2 curves)	1	2- 3- 7- 23-	2- 3-  0 7- -4  0  6  6
Curve Equation t Generators 20286co1 [1,-1,1,15205,3390923] 2 [79:2214:1] 20286co2 [1,-1,1,-267035,49791179] 2 [-47:7912:1]
20286cp (1 curve)	1	2- 3- 7- 23-	2- 3-  1 7- -2 -1  0  2
Curve Equation t Generators 20286cp1 [1,-1,1,263488,-61160893] 1 [331:7723:1]
20286cq (1 curve)	1	2- 3- 7- 23-	2- 3- -1 7- -2  1  0 -2
Curve Equation t Generators 20286cq1 [1,-1,1,5377,176775] 1 [137:-1932:1]
20286cr (2 curves)	1	2- 3- 7- 23-	2- 3- -2 7-  0 -4  0 -6
Curve Equation t Generators 20286cr1 [1,-1,1,147064,50129867] 2 [79:7849:1] 20286cr2 [1,-1,1,-1475816,603207371] 2 [-789:36115:1]
20286cs (2 curves)	1	2- 3- 7- 23-	2- 3- -2 7-  6  2  0  0
Curve Equation t Generators 20286cs1 [1,-1,1,-671,14627] 2 [39:196:1] 20286cs2 [1,-1,1,-13901,633791] 2 [606:539:8]
20286ct (1 curve)	1	2- 3- 7- 23-	2- 3-  3 7- -4 -3  0  0
Curve Equation t Generators 20286ct1 [1,-1,1,-2263001,-1316208967] 1 [1927:37452:1]
20286cu (1 curve)	1	2- 3- 7- 23-	2- 3- -3 7-  2 -3 -3  0
Curve Equation t Generators 20286cu1 [1,-1,1,-104,1019] 1 [3:25:1]

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