Cremona's table of elliptic curves

28314 = 2 · 3² · 11² · 13

Class	r	Atkin-Lehner	Eigenvalues
28314a (2 curves)	1	2+ 3+ 11+ 13+	2+ 3+  2  2 11+ 13+  2  0
Curve Equation t Generators 28314a1 [1,-1,0,-150486,-20753056] 2 [-1690:10889:8] 28314a2 [1,-1,0,-509856,116310662] 2 [209922:-5115181:216]
28314b (2 curves)	2	2+ 3+ 11+ 13-	2+ 3+ -2 -2 11+ 13-  2  0
Curve Equation t Generators 28314b1 [1,-1,0,-138,-544] 2 [-58:77:8]&[-7:10:1] 28314b2 [1,-1,0,-468,3350] 2 [-178:479:8]&[-19:81:1]
28314c (2 curves)	0	2+ 3+ 11- 13+	2+ 3+  0  2 11- 13+  2  6
Curve Equation t 28314c1 [1,-1,0,-143952,20123648] 2 28314c2 [1,-1,0,-405312,-73390960] 2
28314d (1 curve)	0	2+ 3+ 11- 13+	2+ 3+  0  2 11- 13+  8  3
Curve Equation t 28314d1 [1,-1,0,93,-181] 1
28314e (1 curve)	1	2+ 3+ 11- 13-	2+ 3+  0 -2 11- 13-  8 -3
Curve Equation t Generators 28314e1 [1,-1,0,1248,-8090] 1 [17:125:1]
28314f (2 curves)	1	2+ 3+ 11- 13-	2+ 3+  2  2 11- 13-  0  6
Curve Equation t Generators 28314f1 [1,-1,0,-3471,152477] 2 [34:253:1] 28314f2 [1,-1,0,-68811,6960905] 2 [113:730:1]
28314g (2 curves)	1	2+ 3+ 11- 13-	2+ 3+  2  2 11- 13- -8 -2
Curve Equation t Generators 28314g1 [1,-1,0,-1020418251,-12546075035323] 2 [2697923033155426231202027898222471702385103056614792418887460727:-455587798887017641698175780877213946012280875632371200829189349066:51492937307685119732142882511094736699973964764460337696481] 28314g2 [1,-1,0,-16326705291,-802959676523515] 2 [-8127879801077415126213032952070058353:4063682829636680190098802782929701615:110176779828503623470188040686899]
28314h (2 curves)	1	2+ 3+ 11- 13-	2+ 3+ -2  2 11- 13- -4 -2
Curve Equation t Generators 28314h1 [1,-1,0,4152,-839360] 2 [201:2743:1] 28314h2 [1,-1,0,-112008,-13779584] 2 [-195:884:1]
28314i (2 curves)	0	2+ 3- 11+ 13+	2+ 3-  0  0 11+ 13+  0  0
Curve Equation t 28314i1 [1,-1,0,21213,664065] 2 28314i2 [1,-1,0,-98577,5767119] 2
28314j (2 curves)	0	2+ 3- 11+ 13+	2+ 3-  0  0 11+ 13+ -4 -4
Curve Equation t 28314j1 [1,-1,0,423648,279860224] 2 28314j2 [1,-1,0,-4708512,3501830272] 2
28314k (1 curve)	0	2+ 3- 11+ 13+	2+ 3-  3 -3 11+ 13+  2  2
Curve Equation t 28314k1 [1,-1,0,-231138,42858778] 1
28314l (1 curve)	0	2+ 3- 11+ 13+	2+ 3-  3 -3 11+ 13+ -6 -6
Curve Equation t 28314l1 [1,-1,0,-46998,-6351372] 1
28314m (2 curves)	0	2+ 3- 11+ 13+	2+ 3- -4  4 11+ 13+  2  2
Curve Equation t 28314m1 [1,-1,0,-2170944,-992915456] 2 28314m2 [1,-1,0,-32837184,-72414588416] 2
28314n (1 curve)	1	2+ 3- 11+ 13-	2+ 3-  1  1 11+ 13-  2 -6
Curve Equation t Generators 28314n1 [1,-1,0,291,-379] 1 [25:136:1]
28314o (2 curves)	1	2+ 3- 11- 13+	2+ 3-  0 -2 11- 13+  3  4
Curve Equation t Generators 28314o1 [1,-1,0,-10962,443988] 1 [52:86:1] 28314o2 [1,-1,0,-43137,-2996163] 1 [-750958:834231:4913]
28314p (4 curves)	1	2+ 3- 11- 13+	2+ 3-  0  4 11- 13+  0  4
Curve Equation t Generators 28314p1 [1,-1,0,391473,67689837] 2 [-81:5994:1] 28314p2 [1,-1,0,-1960767,602589213] 2 [-1323:30321:1] 28314p3 [1,-1,0,-4067982,-4216062636] 2 [3242952:240750801:512] 28314p4 [1,-1,0,-70976142,-230111392428] 2 [-38898:58527:8]
28314q (1 curve)	1	2+ 3- 11- 13+	2+ 3-  2  2 11- 13+  0  1
Curve Equation t Generators 28314q1 [1,-1,0,-666,6804] 1 [15:-12:1]
28314r (2 curves)	1	2+ 3- 11- 13+	2+ 3-  2 -4 11- 13+  0 -2
Curve Equation t Generators 28314r1 [1,-1,0,-7101,-329103] 2 [1884:80733:1] 28314r2 [1,-1,0,-126891,-17363241] 2 [465:4668:1]
28314s (1 curve)	1	2+ 3- 11- 13+	2+ 3- -2 -2 11- 13+  1  2
Curve Equation t Generators 28314s1 [1,-1,0,-146493,21166789] 1 [138:1819:1]
28314t (1 curve)	1	2+ 3- 11- 13+	2+ 3- -2 -2 11- 13+ -4 -3
Curve Equation t Generators 28314t1 [1,-1,0,522,-162486] 1 [69:411:1]
28314u (4 curves)	1	2+ 3- 11- 13+	2+ 3- -2 -4 11- 13+  2  8
Curve Equation t Generators 28314u1 [1,-1,0,-21258,24911860] 2 [47:-4924:1] 28314u2 [1,-1,0,-1415178,642418420] 4 [-547:35666:1] 28314u3 [1,-1,0,-2547738,-530234204] 2 [-723:30914:1] 28314u4 [1,-1,0,-22585338,41318763844] 2 [2280:39758:1]
28314v (3 curves)	1	2+ 3- 11- 13+	2+ 3-  3  1 11- 13+ -3 -2
Curve Equation t Generators 28314v1 [1,-1,0,522,7398] 1 [398:2947:8] 28314v2 [1,-1,0,-4923,-263763] 1 [3517198:1359087:39304] 28314v3 [1,-1,0,-500418,-136128492] 1 [3630073202614431538:-29788498990830704035:4300687570265848]
28314w (2 curves)	1	2+ 3- 11- 13+	2+ 3- -3  1 11- 13+  0 -2
Curve Equation t Generators 28314w1 [1,-1,0,-113241321,463855087053] 1 [49326:-705:8] 28314w2 [1,-1,0,-87905736,676853506368] 1 [-55218:7844451:8]
28314x (2 curves)	1	2+ 3- 11- 13+	2+ 3- -3  1 11- 13+  6 -8
Curve Equation t Generators 28314x1 [1,-1,0,-7101,1539621] 1 [-129:609:1] 28314x2 [1,-1,0,63684,-40719024] 1 [20916:236745:64]
28314y (2 curves)	0	2+ 3- 11- 13-	2+ 3-  0  2 11- 13- -3  8
Curve Equation t 28314y1 [1,-1,0,-567,-2403] 1 28314y2 [1,-1,0,-22347,1291329] 3
28314z (1 curve)	0	2+ 3- 11- 13-	2+ 3-  1 -1 11- 13- -1  4
Curve Equation t 28314z1 [1,-1,0,-36504,2700616] 1
28314ba (4 curves)	2	2+ 3- 11- 13-	2+ 3- -2  0 11- 13-  2 -4
Curve Equation t Generators 28314ba1 [1,-1,0,5967,-3967331] 2 [155:737:1]&[1894:25189:8] 28314ba2 [1,-1,0,-342513,-74987555] 4 [-379:716:1]&[-301:1028:1] 28314ba3 [1,-1,0,-821673,181554709] 2 [-987:5999:1]&[-415:21443:1] 28314ba4 [1,-1,0,-5439033,-4881005915] 2 [-1347:716:1]&[38453:-7545364:1]
28314bb (1 curve)	0	2+ 3- 11- 13-	2+ 3- -2  2 11- 13- -4  7
Curve Equation t 28314bb1 [1,-1,0,-468,-20696] 1
28314bc (2 curves)	0	2- 3+ 11+ 13+	2- 3+ -2  2 11+ 13+ -2  0
Curve Equation t 28314bc1 [1,-1,1,-16721,774205] 2 28314bc2 [1,-1,1,-56651,-4288919] 2
28314bd (2 curves)	1	2- 3+ 11+ 13-	2- 3+  2 -2 11+ 13- -2  0
Curve Equation t Generators 28314bd1 [1,-1,1,-1244,15931] 2 [254:571:8] 28314bd2 [1,-1,1,-4214,-86237] 2 [958:7967:8]
28314be (2 curves)	1	2- 3+ 11- 13+	2- 3+  0  2 11- 13+ -2  6
Curve Equation t Generators 28314be1 [1,-1,1,-15995,-739989] 2 [179:1362:1] 28314be2 [1,-1,1,-45035,2733195] 2 [201:1230:1]
28314bf (1 curve)	1	2- 3+ 11- 13+	2- 3+  0  2 11- 13+ -8  3
Curve Equation t Generators 28314bf1 [1,-1,1,10,3] 1 [-2:3:8]
28314bg (1 curve)	0	2- 3+ 11- 13-	2- 3+  0 -2 11- 13- -8 -3
Curve Equation t 28314bg1 [1,-1,1,11230,207199] 1
28314bh (2 curves)	0	2- 3+ 11- 13-	2- 3+  2  2 11- 13-  4 -2
Curve Equation t 28314bh1 [1,-1,1,37366,22625353] 2 28314bh2 [1,-1,1,-1008074,373056841] 2
28314bi (2 curves)	0	2- 3+ 11- 13-	2- 3+ -2  2 11- 13-  0  6
Curve Equation t 28314bi1 [1,-1,1,-386,-5519] 2 28314bi2 [1,-1,1,-7646,-255263] 2
28314bj (2 curves)	0	2- 3+ 11- 13-	2- 3+ -2  2 11- 13-  8 -2
Curve Equation t 28314bj1 [1,-1,1,-113379806,464707239021] 2 28314bj2 [1,-1,1,-1814078366,29739851971437] 2
28314bk (1 curve)	1	2- 3- 11+ 13+	2- 3-  1 -1 11+ 13+ -2  6
Curve Equation t Generators 28314bk1 [1,-1,1,35188,398863] 1 [817:23549:1]
28314bl (2 curves)	0	2- 3- 11+ 13-	2- 3-  0  0 11+ 13-  0  0
Curve Equation t 28314bl1 [1,-1,1,175,-547] 2 28314bl2 [1,-1,1,-815,-4111] 2
28314bm (2 curves)	0	2- 3- 11+ 13-	2- 3-  0  0 11+ 13-  4  4
Curve Equation t 28314bm1 [1,-1,1,51261385,-372647742321] 2 28314bm2 [1,-1,1,-569729975,-4659226902129] 2
28314bn (1 curve)	0	2- 3- 11+ 13-	2- 3-  3  3 11+ 13- -2 -2
Curve Equation t 28314bn1 [1,-1,1,-27967721,-56961130377] 1
28314bo (1 curve)	0	2- 3- 11+ 13-	2- 3-  3  3 11+ 13-  6  6
Curve Equation t 28314bo1 [1,-1,1,-5686781,8470736453] 1
28314bp (2 curves)	2	2- 3- 11+ 13-	2- 3- -4 -4 11+ 13- -2 -2
Curve Equation t Generators 28314bp1 [1,-1,1,-17942,750885] 2 [617:14667:1]&[-103:1275:1] 28314bp2 [1,-1,1,-271382,54480165] 2 [305:-261:1]&[-487:8667:1]
28314bq (2 curves)	0	2- 3- 11- 13+	2- 3-  0 -2 11- 13+  3 -8
Curve Equation t 28314bq1 [1,-1,1,-68630,3404261] 1 28314bq2 [1,-1,1,-2704010,-1710646891] 1
28314br (1 curve)	0	2- 3- 11- 13+	2- 3- -1  3 11- 13+ -6  0
Curve Equation t 28314br1 [1,-1,1,-23,-29235] 1
28314bs (2 curves)	0	2- 3- 11- 13+	2- 3- -1 -3 11- 13+  3  0
Curve Equation t 28314bs1 [1,-1,1,304897,9861063] 1 28314bs2 [1,-1,1,-30415793,-64572957237] 1
28314bt (4 curves)	0	2- 3- 11- 13+	2- 3-  2  0 11- 13+  6  0
Curve Equation t 28314bt1 [1,-1,1,-167729,30780753] 2 28314bt2 [1,-1,1,-2803109,1807026873] 4 28314bt3 [1,-1,1,-2922899,1644256221] 2 28314bt4 [1,-1,1,-44849399,115617924645] 2
28314bu (1 curve)	0	2- 3- 11- 13+	2- 3- -2 -2 11- 13+  4 -7
Curve Equation t 28314bu1 [1,-1,1,-56651,27716307] 1
28314bv (1 curve)	0	2- 3- 11- 13+	2- 3-  3 -1 11- 13+ -8  6
Curve Equation t 28314bv1 [1,-1,1,-622931,4273910259] 1
28314bw (1 curve)	0	2- 3- 11- 13+	2- 3-  3  5 11- 13+  7  0
Curve Equation t 28314bw1 [1,-1,1,14134,6169353] 1
28314bx (2 curves)	0	2- 3- 11- 13+	2- 3-  3 -5 11- 13+  0 -2
Curve Equation t 28314bx1 [1,-1,1,14134,-1443967] 1 28314bx2 [1,-1,1,-671936,-212204671] 1
28314by (2 curves)	0	2- 3- 11- 13+	2- 3- -4  0 11- 13+  0  0
Curve Equation t 28314by1 [1,-1,1,-2505812,-1532807625] 2 28314by2 [1,-1,1,-40141652,-97880558025] 2
28314bz (2 curves)	1	2- 3- 11- 13-	2- 3-  0  2 11- 13- -3 -4
Curve Equation t Generators 28314bz1 [1,-1,1,-1326425,-586968775] 1 [-665:1164:1] 28314bz2 [1,-1,1,-5219600,4003551731] 3 [-60389:24081735:343]
28314ca (1 curve)	1	2- 3- 11- 13-	2- 3-  1 -1 11- 13-  2  4
Curve Equation t Generators 28314ca1 [1,-1,1,-71897,-10235343] 1 [10805:1117356:1]
28314cb (2 curves)	1	2- 3- 11- 13-	2- 3-  1 -1 11- 13- -3 -6
Curve Equation t Generators 28314cb1 [1,-1,1,-2927,93943] 1 [47:218:1] 28314cb2 [1,-1,1,-231617,-47016197] 1 [4534:12733:8]
28314cc (2 curves)	1	2- 3- 11- 13-	2- 3-  1 -1 11- 13-  4 -6
Curve Equation t Generators 28314cc1 [1,-1,1,-6288322712,192138899879963] 1 [-30357:18858145:1] 28314cc2 [1,-1,1,17808513898,-12058462656159037] 1 [43726798246842:-97847852820645181:8741816]
28314cd (1 curve)	1	2- 3- 11- 13-	2- 3-  1  3 11- 13- -4  2
Curve Equation t Generators 28314cd1 [1,-1,1,-50117,4553277] 1 [311:4200:1]
28314ce (1 curve)	1	2- 3- 11- 13-	2- 3-  2 -2 11- 13-  0 -1
Curve Equation t Generators 28314ce1 [1,-1,1,-80609,-8814319] 1 [333:922:1]
28314cf (1 curve)	1	2- 3- 11- 13-	2- 3- -2  2 11- 13- -1 -2
Curve Equation t Generators 28314cf1 [1,-1,1,-1211,-15573] 1 [-21:26:1]
28314cg (1 curve)	1	2- 3- 11- 13-	2- 3- -2  2 11- 13-  4  3
Curve Equation t Generators 28314cg1 [1,-1,1,63139,216079427] 1 [-3618:79727:8]
28314ch (4 curves)	1	2- 3- 11- 13-	2- 3- -2 -4 11- 13-  2  4
Curve Equation t Generators 28314ch1 [1,-1,1,-1161986,481766145] 4 [663:1241:1] 28314ch2 [1,-1,1,-1510466,169249281] 4 [-613:29709:1] 28314ch3 [1,-1,1,5851174,1329443745] 2 [1415:110829:1] 28314ch4 [1,-1,1,-14447786,-20996206239] 2 [-2065:6477:1]
28314ci (2 curves)	1	2- 3- 11- 13-	2- 3- -2 -4 11- 13- -8  6
Curve Equation t Generators 28314ci1 [1,-1,1,-361571,-214537309] 2 [1587:-57422:1] 28314ci2 [1,-1,1,-8028131,-8742818653] 2 [-1625:3958:1]
28314cj (2 curves)	1	2- 3- 11- 13-	2- 3- -4  4 11- 13-  4  4
Curve Equation t Generators 28314cj1 [1,-1,1,-1112,-248245] 2 [1278:14603:8] 28314cj2 [1,-1,1,-66452,-6520885] 2 [-147:307:1]

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