Cremona's table of elliptic curves

82810 = 2 · 5 · 7² · 13²

Class	r	Atkin-Lehner	Eigenvalues
82810a (2 curves)	1	2+ 5+ 7+ 13+	2+  1 5+ 7+  0 13+  0 -2
Curve Equation t Generators 82810a1 [1,0,1,-75365554,-293684405948] 1 [87283724154557070572901306904975:2670149525034192696513455172327619:8201984524143956621510954219] 82810a2 [1,0,1,-6382175154,-196246703864508] 1 [207527145457723915551814126167248810794957311390533215076256347056613122593421705103378685:56664447233310302314647976063653019333760119781757499641868889035708761911474275129709069417:1553402151921635135710243890082158325017938437414222221677507769231884670681946482657]
82810b (1 curve)	1	2+ 5+ 7+ 13+	2+  1 5+ 7+  4 13+  0  6
Curve Equation t Generators 82810b1 [1,0,1,-49859,4323022] 1 [235:2248:1]
82810c (1 curve)	0	2+ 5+ 7- 13+	2+  0 5+ 7-  1 13+  4 -8
Curve Equation t 82810c1 [1,-1,0,1405,-28798379] 1
82810d (2 curves)	0	2+ 5+ 7- 13+	2+  0 5+ 7-  3 13+ -4  0
Curve Equation t 82810d1 [1,-1,0,40,-64] 1 82810d2 [1,-1,0,-13610,614550] 1
82810e (4 curves)	0	2+ 5+ 7- 13+	2+  0 5+ 7- -4 13+ -2  0
Curve Equation t 82810e1 [1,-1,0,19150,1620100] 2 82810e2 [1,-1,0,-146470,17486496] 4 82810e3 [1,-1,0,-726140,-222380950] 2 82810e4 [1,-1,0,-2216720,1270815846] 2
82810f (2 curves)	0	2+ 5+ 7- 13+	2+  0 5+ 7-  6 13+  8  0
Curve Equation t 82810f1 [1,-1,0,-280706750,-1665851375980] 2 82810f2 [1,-1,0,312875330,-7772505098604] 2
82810g (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7- -3 13+  0 -8
Curve Equation t 82810g1 [1,0,1,-741914,-246108614] 1
82810h (1 curve)	0	2+ 5+ 7- 13+	2+  1 5+ 7-  5 13+ -2 -6
Curve Equation t 82810h1 [1,0,1,-1623249,-4454382684] 1
82810i (2 curves)	0	2+ 5+ 7- 13+	2+ -1 5+ 7-  0 13+  3 -4
Curve Equation t 82810i1 [1,1,0,20212,-4403888] 1 82810i2 [1,1,0,-183628,125523728] 1
82810j (1 curve)	2	2+ 5+ 7- 13+	2+ -1 5+ 7-  1 13+ -4  0
Curve Equation t Generators 82810j1 [1,1,0,-688678,242954132] 1 [-589:21382:1]&[629:7375:1]
82810k (2 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7-  0 13+  0 -1
Curve Equation t 82810k1 [1,1,0,192,512] 1 82810k2 [1,1,0,-3448,78408] 1
82810l (6 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7-  0 13+  0  2
Curve Equation t 82810l1 [1,1,0,-9904248,-11955512512] 2 82810l2 [1,1,0,-158299768,-766665448128] 2 82810l3 [1,1,0,-54952888,147851092992] 2 82810l4 [1,1,0,-168568208,-661567169752] 2 82810l5 [1,1,0,-4380450428,111588429414428] 2 82810l6 [1,1,0,-4381030098,111557418344702] 2
82810m (2 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7- -3 13+  3 -1
Curve Equation t 82810m1 [1,1,0,-25360143,-49171600603] 1 82810m2 [1,1,0,3410417,-152370993627] 1
82810n (2 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7- -3 13+ -6 -1
Curve Equation t 82810n1 [1,1,0,-8453,11236373] 1 82810n2 [1,1,0,-4066143,3154323047] 1
82810o (2 curves)	0	2+ 5+ 7- 13+	2+  2 5+ 7-  4 13+  8  6
Curve Equation t 82810o1 [1,1,0,-588123,-204400867] 2 82810o2 [1,1,0,-9862843,-11925792003] 2
82810p (2 curves)	0	2+ 5+ 7- 13+	2+ -2 5+ 7-  2 13+ -2  6
Curve Equation t 82810p1 [1,0,1,-6964494,7072736192] 2 82810p2 [1,0,1,-6302014,8472423936] 2
82810q (2 curves)	2	2+ 5+ 7- 13+	2+ -2 5+ 7- -4 13+  0 -2
Curve Equation t Generators 82810q1 [1,0,1,-49859,-1274934] 2 [-206:617:1]&[-181:1442:1] 82810q2 [1,0,1,-629529,-192102298] 2 [-454:649:1]&[21718:1065667:8]
82810r (1 curve)	0	2+ 5+ 7- 13+	2+  3 5+ 7- -3 13+  2 -6
Curve Equation t 82810r1 [1,-1,0,-270685,-55013659] 1
82810s (2 curves)	0	2+ 5+ 7- 13+	2+ -3 5+ 7-  2 13+  4 -6
Curve Equation t 82810s1 [1,-1,0,-22255,-1272335] 1 82810s2 [1,-1,0,155195,12086101] 1
82810t (2 curves)	1	2+ 5+ 7- 13-	2+  0 5+ 7- -2 13- -6  6
Curve Equation t Generators 82810t1 [1,-1,0,-477710,115533536] 2 [520:2484:1] 82810t2 [1,-1,0,598820,561001650] 2 [-28236:943305:64]
82810u (2 curves)	1	2+ 5+ 7- 13-	2+  0 5+ 7-  4 13-  0 -6
Curve Equation t Generators 82810u1 [1,-1,0,-1060565,-419428619] 2 [9830:86813:8] 82810u2 [1,-1,0,-1417285,-112578075] 2 [-614:23239:1]
82810v (1 curve)	0	2+ 5- 7+ 13+	2+  0 5- 7+  1 13+ -4  8
Curve Equation t 82810v1 [1,-1,0,68836,9877706320] 1
82810w (2 curves)	0	2+ 5- 7+ 13+	2+  0 5- 7+  3 13+  4  0
Curve Equation t 82810w1 [1,-1,0,1951,18045] 1 82810w2 [1,-1,0,-666899,-209456857] 1
82810x (2 curves)	0	2+ 5- 7+ 13+	2+ -2 5- 7+  0 13+  0  1
Curve Equation t 82810x1 [1,0,1,9382,-147444] 1 82810x2 [1,0,1,-168978,-27400852] 1
82810y (2 curves)	0	2+ 5- 7+ 13+	2+ -2 5- 7+ -3 13+ -3  1
Curve Equation t 82810y1 [1,0,1,-1242647033,16862131065756] 1 82810y2 [1,0,1,167110407,52263752145308] 1
82810z (2 curves)	0	2+ 5- 7+ 13+	2+ -2 5- 7+ -3 13+  6  1
Curve Equation t 82810z1 [1,0,1,-173,-32784] 1 82810z2 [1,0,1,-82983,-9208132] 1
82810ba (2 curves)	0	2+ 5- 7+ 13+	2+  3 5- 7+  2 13+ -4  6
Curve Equation t 82810ba1 [1,-1,0,-1090504,438591908] 1 82810ba2 [1,-1,0,7604546,-4160741740] 1
82810bb (4 curves)	1	2+ 5- 7- 13+	2+  0 5- 7-  0 13+ -2 -8
Curve Equation t Generators 82810bb1 [1,-1,0,-55379,1827125] 2 [569:12137:1] 82810bb2 [1,-1,0,-717859,234092613] 4 [282:7209:1] 82810bb3 [1,-1,0,-552239,344826145] 2 [-159:20782:1] 82810bb4 [1,-1,0,-11483159,14980400553] 2 [1388:40711:1]
82810bc (2 curves)	1	2+ 5- 7- 13+	2+  0 5- 7-  3 13+  4  7
Curve Equation t Generators 82810bc1 [1,-1,0,-7259849,-12267898707] 1 [284943551:57807231180:6859] 82810bc2 [1,-1,0,-637029899,6689549044933] 1 [14964319627274825780051462974842051643088524228624375967931152126841639897:2714184822593193430471372582684413210993624532005983605158887861539537292225:339422513285390673186040338501982654125640465959531973989531732906713]
82810bd (1 curve)	1	2+ 5- 7- 13+	2+  1 5- 7-  1 13+  4  0
Curve Equation t Generators 82810bd1 [1,0,1,-33745248,-83434502994] 1 [4218213570:2481251801029:12167]
82810be (2 curves)	1	2+ 5- 7- 13+	2+ -1 5- 7-  0 13+  0  2
Curve Equation t Generators 82810be1 [1,1,0,-1538072,855563584] 1 [14448:1723336:1] 82810be2 [1,1,0,-130248472,572092003904] 1 [15904:1580648:1]
82810bf (2 curves)	1	2+ 5- 7- 13+	2+ -1 5- 7-  0 13+  3  4
Curve Equation t Generators 82810bf1 [1,1,0,-82390153472,-9102542581769216] 1 [13346804787981408984416:-2796342531499303979487488:37957785596021017] 82810bf2 [1,1,0,-82368084607,-9107662613459899] 1 [214538318294:251872608831253:148877]
82810bg (2 curves)	1	2+ 5- 7- 13+	2+ -1 5- 7-  0 13+  3 -8
Curve Equation t Generators 82810bg1 [1,1,0,-172,230924] 1 [-50:368:1] 82810bg2 [1,1,0,-290007,59994901] 1 [342:809:1]
82810bh (1 curve)	1	2+ 5- 7- 13+	2+ -1 5- 7- -3 13+  0  8
Curve Equation t Generators 82810bh1 [1,1,0,-36353762,84378900754] 1 [9183:719996:1]
82810bi (1 curve)	1	2+ 5- 7- 13+	2+ -1 5- 7-  4 13+  0 -6
Curve Equation t Generators 82810bi1 [1,1,0,-2443067,-1485239699] 1 [21421744950:4814178998339:421875]
82810bj (2 curves)	1	2+ 5- 7- 13+	2+  2 5- 7-  3 13+  6 -5
Curve Equation t Generators 82810bj1 [1,1,0,-82982,-9706276] 1 [49185897176860832553637175666109885665:1440593383569576636857083080888347974358:50148013774166229400315220269914839] 82810bj2 [1,1,0,455283,-15196579] 1 [636335265223:59049666850546:73560059]
82810bk (2 curves)	1	2+ 5- 7- 13+	2+  2 5- 7-  4 13+  0 -6
Curve Equation t Generators 82810bk1 [1,1,0,-9481917,-9137546179] 2 [-39255:1092017:27] 82810bk2 [1,1,0,-46580797,114127192509] 2 [2085:160437:1]
82810bl (2 curves)	1	2+ 5- 7- 13+	2+ -2 5- 7-  4 13+ -8 -6
Curve Equation t Generators 82810bl1 [1,0,1,-12003,594206] 2 [40:-443:1] 82810bl2 [1,0,1,-201283,34740318] 2 [274:-560:1]
82810bm (1 curve)	1	2+ 5- 7- 13+	2+  3 5- 7-  4 13+ -5 -2
Curve Equation t Generators 82810bm1 [1,-1,0,275861,237173] 1 [894:82363:27]
82810bn (1 curve)	0	2+ 5- 7- 13-	2+ -1 5- 7-  5 13-  6  8
Curve Equation t 82810bn1 [1,1,0,993548,1213662416] 1
82810bo (2 curves)	2	2+ 5- 7- 13-	2+ -2 5- 7-  0 13- -6  0
Curve Equation t Generators 82810bo1 [1,0,1,-3358,28368] 2 [-3:197:1]&[-51:285:1] 82810bo2 [1,0,1,-28838,-1867344] 2 [-100:187:1]&[-94:169:1]
82810bp (1 curve)	0	2- 5+ 7+ 13+	2-  0 5+ 7+ -1 13+ -4 -8
Curve Equation t 82810bp1 [1,-1,1,11633252,21701355684831] 1
82810bq (2 curves)	0	2- 5+ 7+ 13+	2-  0 5+ 7+ -3 13+  4  0
Curve Equation t 82810bq1 [1,-1,1,329687,40633961] 1 82810bq2 [1,-1,1,-112705963,-460514832683] 1
82810br (2 curves)	0	2- 5+ 7+ 13+	2- -2 5+ 7+  0 13+  0 -1
Curve Equation t 82810br1 [1,0,0,1585639,-325519559] 3 82810br2 [1,0,0,-28557201,-60171114095] 1
82810bs (2 curves)	0	2- 5+ 7+ 13+	2- -2 5+ 7+ -3 13+ -6  1
Curve Equation t 82810bs1 [1,0,0,136464,25586560] 1 82810bs2 [1,0,0,-1312711,-1005356535] 1
82810bt (2 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7-  0 13+  6  4
Curve Equation t Generators 82810bt1 [1,-1,1,39852,10375187] 2 [713867934296:-49005509720231:153990656] 82810bt2 [1,-1,1,-539818,139757531] 2 [735875338:-4672031131:2406104]
82810bu (2 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7- -3 13+  4 -7
Curve Equation t Generators 82810bu1 [1,-1,1,-42958,-5574019] 1 [120029:1554253:343] 82810bu2 [1,-1,1,-3769408,3045726051] 1 [573:32481:1]
82810bv (4 curves)	1	2- 5+ 7- 13+	2-  0 5+ 7- -4 13+ -2 -4
Curve Equation t Generators 82810bv1 [1,-1,1,-16563553,-23733322063] 2 [-2665:39748:1] 82810bv2 [1,-1,1,-58962273,147777980081] 4 [-38946:4540895:8] 82810bv3 [1,-1,1,106657727,828211188081] 2 [59035548:11477847701:1728] 82810bv4 [1,-1,1,-902961793,10443559324657] 2 [10550716932:55170892057:592704]
82810bw (2 curves)	1	2- 5+ 7- 13+	2- -1 5+ 7-  0 13+  3 -4
Curve Equation t Generators 82810bw1 [1,1,1,-487515701,-4143356637477] 1 [39494384536473:1787274591348484:1493271207] 82810bw2 [1,1,1,-487385116,-4145687052291] 1 [691167:10232131:27]
82810bx (2 curves)	1	2- 5+ 7- 13+	2- -1 5+ 7-  0 13+  3  8
Curve Equation t Generators 82810bx1 [1,1,1,-29156,507485649] 1 [9404401:28835396163:1] 82810bx2 [1,1,1,-49011271,132053853693] 1 [3849:19292:1]
82810by (2 curves)	1	2- 5+ 7- 13+	2- -1 5+ 7-  3 13+  6  2
Curve Equation t Generators 82810by1 [1,1,1,53654,-31408707] 1 [2215422:37561643:5832] 82810by2 [1,1,1,-484611,865556089] 1 [27903:1021160:27]
82810bz (2 curves)	1	2- 5+ 7- 13+	2- -1 5+ 7-  6 13+  0  2
Curve Equation t Generators 82810bz1 [1,1,1,419,-57] 1 [239:3598:1] 82810bz2 [1,1,1,-5496,167929] 1 [31:-185:1]
82810ca (4 curves)	1	2- 5+ 7- 13+	2-  2 5+ 7-  0 13+  0  2
Curve Equation t Generators 82810ca1 [1,1,1,-1933786,-1034486237] 2 [-1872072504882:1962756144307:2268747144] 82810ca2 [1,1,1,-2513456,-363923981] 2 [920986352813246577066:-229856958555913727504711:14835798130286232] 82810ca3 [1,1,1,-7854701,7460627299] 2 [558641:417256980:1] 82810ca4 [1,1,1,-121470021,515230215443] 2 [15084399:11265126376:27]
82810cb (2 curves)	1	2- 5+ 7- 13+	2-  2 5+ 7-  3 13+  3 -7
Curve Equation t Generators 82810cb1 [1,1,1,-3051721,-2644014521] 1 [657047348:2953845505:314432] 82810cb2 [1,1,1,23323264,27328518433] 1 [10181:1143909:1]
82810cc (2 curves)	1	2- 5+ 7- 13+	2-  2 5+ 7- -3 13+  6  5
Curve Equation t Generators 82810cc1 [1,1,1,-491,-4607] 1 [15809:1979898:1] 82810cc2 [1,1,1,2694,-5881] 1 [21:235:1]
82810cd (1 curve)	1	2- 5+ 7- 13+	2-  3 5+ 7- -4 13+ -5  2
Curve Equation t Generators 82810cd1 [1,-1,1,1632,-269] 1 [201:2875:27]
82810ce (1 curve)	2	2- 5+ 7- 13-	2- -1 5+ 7- -5 13-  6 -8
Curve Equation t Generators 82810ce1 [1,1,1,5879,554679] 1 [83:1232:1]&[-218:5005:8]
82810cf (2 curves)	0	2- 5+ 7- 13-	2- -2 5+ 7-  0 13- -6  0
Curve Equation t 82810cf1 [1,0,0,-567421,62892465] 2 82810cf2 [1,0,0,-4873541,-4097680679] 2
82810cg (2 curves)	1	2- 5- 7+ 13+	2-  1 5- 7+  6 13+  0 -2
Curve Equation t Generators 82810cg1 [1,0,0,20530,81080] 1 [58660772:1051272852:226981] 82810cg2 [1,0,0,-269305,-58407623] 1 [2484:119593:1]
82810ch (2 curves)	1	2- 5- 7+ 13+	2- -2 5- 7+  3 13+ -3  7
Curve Equation t Generators 82810ch1 [1,0,0,-62280,7699600] 1 [222:2086:1] 82810ch2 [1,0,0,475985,-79606983] 1 [1574:-68387:1]
82810ci (2 curves)	0	2- 5- 7- 13+	2-  0 5- 7-  0 13+ -6 -4
Curve Equation t 82810ci1 [1,-1,1,813,-30481] 2 82810ci2 [1,-1,1,-11017,-404309] 2
82810cj (1 curve)	0	2- 5- 7- 13+	2-  0 5- 7- -1 13+  4  8
Curve Equation t 82810cj1 [1,-1,1,237413,-63269326389] 1
82810ck (2 curves)	0	2- 5- 7- 13+	2-  0 5- 7-  2 13+  4 -4
Curve Equation t 82810ck1 [1,-1,1,-241702,40965201] 2 82810ck2 [1,-1,1,337968,206982689] 2
82810cl (2 curves)	0	2- 5- 7- 13+	2-  0 5- 7- -3 13+ -4  0
Curve Equation t 82810cl1 [1,-1,1,6728,-120389] 1 82810cl2 [1,-1,1,-2300122,1343266019] 1
82810cm (2 curves)	0	2- 5- 7- 13+	2- -1 5- 7-  0 13+  3  4
Curve Equation t 82810cm1 [1,1,1,3415740,-9692420795] 1 82810cm2 [1,1,1,-31033220,275930796357] 1
82810cn (3 curves)	0	2- 5- 7- 13+	2- -1 5- 7-  3 13+ -6  2
Curve Equation t 82810cn1 [1,1,1,-4790123920,-138367791287055] 1 82810cn2 [1,1,1,29498391705,126928017900445] 1 82810cn3 [1,1,1,-418216978670,110400698894173995] 1
82810co (2 curves)	0	2- 5- 7- 13+	2-  2 5- 7-  0 13+  0  1
Curve Equation t 82810co1 [1,1,1,32360,962905] 1 82810co2 [1,1,1,-582800,175176217] 1
82810cp (2 curves)	0	2- 5- 7- 13+	2-  2 5- 7- -3 13+  6 -1
Curve Equation t 82810cp1 [1,1,1,2785,-73403] 1 82810cp2 [1,1,1,-26790,2919587] 1
82810cq (4 curves)	0	2- 5- 7- 13+	2-  2 5- 7-  6 13+  6  2
Curve Equation t 82810cq1 [1,1,1,-269305,-53585225] 2 82810cq2 [1,1,1,-103685,-118574513] 2 82810cq3 [1,1,1,-1718480,831570865] 2 82810cq4 [1,1,1,931440,3167740337] 2
82810cr (2 curves)	1	2- 5- 7- 13-	2-  0 5- 7-  2 13- -6 -6
Curve Equation t Generators 82810cr1 [1,-1,1,-2827,53239] 2 [1822:25839:8] 82810cr2 [1,-1,1,3543,254531] 2 [-556:30471:64]
82810cs (2 curves)	1	2- 5- 7- 13-	2-  0 5- 7- -4 13-  0  6
Curve Equation t Generators 82810cs1 [1,-1,1,-179235517,-922022382459] 2 [-7929:28464:1] 82810cs2 [1,-1,1,-239521197,-248052594331] 2 [207377:-94275564:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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