Cremona's table of elliptic curves

67760 = 2⁴ · 5 · 7 · 11²

Class	r	Atkin-Lehner	Eigenvalues
67760a (2 curves)	1	2+ 5+ 7+ 11+	2+  0 5+ 7+ 11+ -4 -4 -4
Curve Equation t Generators 67760a1 [0,0,0,-3223,70422] 2 [34:12:1] 67760a2 [0,0,0,-3443,60258] 2 [11:154:1]
67760b (2 curves)	1	2+ 5+ 7+ 11+	2+  2 5+ 7+ 11+ -6  2 -8
Curve Equation t Generators 67760b1 [0,-1,0,-4205516,-3466479520] 2 [50545278616667825893388860348469903174499579:13384682521373711470339294235106190453631408068:720185102030937750732630848001990799431] 67760b2 [0,-1,0,-68120136,-216378861664] 2 [22803588754491034126406:12077038045097244361101750:81228305350270441]
67760c (4 curves)	0	2+ 5+ 7+ 11-	2+  0 5+ 7+ 11- -2 -2  0
Curve Equation t 67760c1 [0,0,0,6284377,-3387211322] 2 67760c2 [0,0,0,-29146843,-29032328358] 4 67760c3 [0,0,0,-230021363,1322813016338] 2 67760c4 [0,0,0,-395171843,-3022165163358] 2
67760d (1 curve)	0	2+ 5+ 7+ 11-	2+  1 5+ 7+ 11- -1 -3 -6
Curve Equation t 67760d1 [0,1,0,-161,6059] 1
67760e (1 curve)	0	2+ 5+ 7+ 11-	2+ -1 5+ 7+ 11-  1 -2 -1
Curve Equation t 67760e1 [0,-1,0,80304,-18742304] 1
67760f (2 curves)	0	2+ 5+ 7+ 11-	2+  2 5+ 7+ 11-  0 -4 -4
Curve Equation t 67760f1 [0,-1,0,5284,-21184] 2 67760f2 [0,-1,0,-21336,-148960] 2
67760g (2 curves)	0	2+ 5+ 7- 11+	2+  0 5+ 7- 11+  4  4  4
Curve Equation t 67760g1 [0,0,0,-389983,-93731682] 2 67760g2 [0,0,0,-416603,-80203398] 2
67760h (2 curves)	0	2+ 5+ 7- 11+	2+  2 5+ 7- 11+  6 -2  8
Curve Equation t 67760h1 [0,-1,0,-34756,2617056] 2 67760h2 [0,-1,0,-562976,162773360] 2
67760i (1 curve)	1	2+ 5+ 7- 11-	2+ -1 5+ 7- 11- -1  2  1
Curve Equation t Generators 67760i1 [0,-1,0,664,13840] 1 [8:-140:1]
67760j (2 curves)	0	2+ 5- 7+ 11+	2+  0 5- 7+ 11+  2  2  2
Curve Equation t 67760j1 [0,0,0,30613,-5475734] 2 67760j2 [0,0,0,-342067,-68607726] 2
67760k (1 curve)	1	2+ 5- 7+ 11-	2+  1 5- 7+ 11-  5  6  1
Curve Equation t Generators 67760k1 [0,1,0,-40,-3500] 1 [18:44:1]
67760l (1 curve)	1	2+ 5- 7+ 11-	2+ -1 5- 7+ 11- -3  4 -1
Curve Equation t Generators 67760l1 [0,-1,0,-9280,349472] 1 [74:250:1]
67760m (2 curves)	1	2+ 5- 7+ 11-	2+  2 5- 7+ 11- -6 -2  2
Curve Equation t Generators 67760m1 [0,-1,0,-40,-106368] 2 [11670:104202:125] 67760m2 [0,-1,0,-33920,-2356000] 2 [796:21780:1]
67760n (1 curve)	1	2+ 5- 7+ 11-	2+  3 5- 7+ 11- -3  0 -5
Curve Equation t Generators 67760n1 [0,0,0,-22627,-1376254] 1 [4719:2420:27]
67760o (2 curves)	1	2+ 5- 7- 11+	2+  0 5- 7- 11+ -2 -2 -2
Curve Equation t Generators 67760o1 [0,0,0,253,4114] 2 [3:-70:1] 67760o2 [0,0,0,-2827,51546] 2 [-33:330:1]
67760p (4 curves)	0	2+ 5- 7- 11-	2+  0 5- 7- 11-  2 -2  0
Curve Equation t 67760p1 [0,0,0,-5687,407286] 2 67760p2 [0,0,0,-124267,16842474] 4 67760p3 [0,0,0,-158147,6929186] 2 67760p4 [0,0,0,-1987667,1078607794] 2
67760q (4 curves)	0	2+ 5- 7- 11-	2+  0 5- 7- 11-  6 -6 -4
Curve Equation t 67760q1 [0,0,0,-14762,491139] 2 67760q2 [0,0,0,-87967,-9655074] 4 67760q3 [0,0,0,45133,-36301694] 4 67760q4 [0,0,0,-1392347,-632366086] 2
67760r (1 curve)	0	2+ 5- 7- 11-	2+  1 5- 7- 11- -5 -6 -1
Curve Equation t 67760r1 [0,1,0,-4880,4639028] 1
67760s (1 curve)	0	2+ 5- 7- 11-	2+ -1 5- 7- 11-  3 -4  1
Curve Equation t 67760s1 [0,-1,0,-1122920,-460655600] 1
67760t (1 curve)	0	2+ 5- 7- 11-	2+  3 5- 7- 11-  3  0  5
Curve Equation t 67760t1 [0,0,0,-187,1034] 1
67760u (1 curve)	0	2+ 5- 7- 11-	2+  3 5- 7- 11-  5  7 -2
Curve Equation t 67760u1 [0,0,0,-49852,4413596] 1
67760v (2 curves)	0	2- 5+ 7+ 11+	2-  0 5+ 7+ 11+  0  0  0
Curve Equation t 67760v1 [0,0,0,6512,72963] 2 67760v2 [0,0,0,-27863,602338] 2
67760w (2 curves)	0	2- 5+ 7+ 11+	2-  0 5+ 7+ 11+ -4  4 -4
Curve Equation t 67760w1 [0,0,0,-967483,-358261398] 2 67760w2 [0,0,0,-15385403,-23227966102] 2
67760x (2 curves)	0	2- 5+ 7+ 11+	2-  0 5+ 7+ 11+  6 -6  6
Curve Equation t 67760x1 [0,0,0,-97163,12561978] 2 67760x2 [0,0,0,-1587883,770145882] 2
67760y (2 curves)	0	2- 5+ 7+ 11+	2-  2 5+ 7+ 11+ -2 -2 -4
Curve Equation t 67760y1 [0,-1,0,1038624,41610560] 2 67760y2 [0,-1,0,-4178896,337965696] 2
67760z (2 curves)	0	2- 5+ 7+ 11+	2-  2 5+ 7+ 11+ -2 -2  8
Curve Equation t 67760z1 [0,-1,0,664,-2704] 2 67760z2 [0,-1,0,-2856,-19600] 2
67760ba (4 curves)	1	2- 5+ 7+ 11-	2-  0 5+ 7+ 11-  6 -2  0
Curve Equation t Generators 67760ba1 [0,0,0,4477,-183678] 2 [231:3630:1] 67760ba2 [0,0,0,-34243,-1972542] 4 [-129:546:1] 67760ba3 [0,0,0,-169763,25158562] 2 [297:968:1] 67760ba4 [0,0,0,-518243,-143590942] 2 [50061:1959958:27]
67760bb (1 curve)	1	2- 5+ 7+ 11-	2-  1 5+ 7+ 11- -1 -4 -3
Curve Equation t Generators 67760bb1 [0,1,0,27064,53960564] 1 [2564:130330:1]
67760bc (2 curves)	1	2- 5+ 7+ 11-	2- -1 5+ 7+ 11- -1  6  7
Curve Equation t Generators 67760bc1 [0,-1,0,-79416,-14589584] 1 [14298:595945:8] 67760bc2 [0,-1,0,665944,264473200] 1 [-1046:105875:8]
67760bd (2 curves)	1	2- 5+ 7+ 11-	2- -1 5+ 7+ 11-  5  6 -5
Curve Equation t Generators 67760bd1 [0,-1,0,-6816,-214784] 1 [96:80:1] 67760bd2 [0,-1,0,12544,-1097600] 1 [488:11000:1]
67760be (2 curves)	1	2- 5+ 7+ 11-	2- -1 5+ 7+ 11- -7 -6 -5
Curve Equation t Generators 67760be1 [0,-1,0,-15359296,23949777920] 1 [1888:-40960:1] 67760be2 [0,-1,0,-1255638336,17125985729536] 1 [16416:968000:1]
67760bf (2 curves)	1	2- 5+ 7+ 11-	2-  2 5+ 7+ 11-  2  3  7
Curve Equation t Generators 67760bf1 [0,-1,0,-345616,-253637184] 1 [21734598525226920:315064017727464448:24044979331647] 67760bf2 [0,-1,0,3061744,6269412800] 1 [4745016:400562272:729]
67760bg (1 curve)	1	2- 5+ 7+ 11-	2- -3 5+ 7+ 11-  3  1  6
Curve Equation t Generators 67760bg1 [0,0,0,3872,282172] 1 [-46:82:1]
67760bh (2 curves)	1	2- 5+ 7- 11+	2-  0 5+ 7- 11+  0  0  0
Curve Equation t Generators 67760bh1 [0,0,0,787952,-97113753] 2 [437928772:-19131249375:314432] 67760bh2 [0,0,0,-3371423,-801711878] 2 [-5982:288575:8]
67760bi (2 curves)	1	2- 5+ 7- 11+	2-  0 5+ 7- 11+  4 -4  4
Curve Equation t Generators 67760bi1 [0,0,0,-117065443,476845920738] 2 [19847952:626075415:4096] 67760bi2 [0,0,0,-1861633763,30916422881762] 2 [24478:117880:1]
67760bj (2 curves)	1	2- 5+ 7- 11+	2-  0 5+ 7- 11+ -6  6 -6
Curve Equation t Generators 67760bj1 [0,0,0,-803,-9438] 2 [47:238:1] 67760bj2 [0,0,0,-13123,-578622] 2 [223:2754:1]
67760bk (2 curves)	1	2- 5+ 7- 11+	2-  2 5+ 7- 11+  2  2  4
Curve Equation t Generators 67760bk1 [0,-1,0,8584,-34384] 2 [130:1806:1] 67760bk2 [0,-1,0,-34536,-241360] 2 [5358:22274:27]
67760bl (2 curves)	1	2- 5+ 7- 11+	2-  2 5+ 7- 11+  2  2 -8
Curve Equation t Generators 67760bl1 [0,-1,0,80304,3277760] 2 [485580:11966255:1728] 67760bl2 [0,-1,0,-345616,27470016] 2 [-171:9030:1]
67760bm (1 curve)	0	2- 5+ 7- 11-	2-  1 5+ 7- 11-  1  4  3
Curve Equation t 67760bm1 [0,1,0,224,-40460] 1
67760bn (2 curves)	2	2- 5+ 7- 11-	2- -1 5+ 7- 11-  1 -6 -7
Curve Equation t Generators 67760bn1 [0,-1,0,-656,11200] 1 [18:70:1]&[-24:112:1] 67760bn2 [0,-1,0,5504,-200704] 1 [64:640:1]&[106:1250:1]
67760bo (3 curves)	0	2- 5+ 7- 11-	2- -1 5+ 7- 11- -5 -3  2
Curve Equation t 67760bo1 [0,-1,0,-2581,56861] 1 67760bo2 [0,-1,0,16779,-148355] 1 67760bo3 [0,-1,0,-254261,-51537539] 1
67760bp (2 curves)	0	2- 5+ 7- 11-	2- -1 5+ 7- 11- -5 -6  5
Curve Equation t 67760bp1 [0,-1,0,-824776,289176560] 1 67760bp2 [0,-1,0,1517784,1454834416] 1
67760bq (2 curves)	0	2- 5+ 7- 11-	2- -1 5+ 7- 11-  7  6  5
Curve Equation t 67760bq1 [0,-1,0,-126936,-17947664] 1 67760bq2 [0,-1,0,-10377176,-12863233040] 1
67760br (2 curves)	0	2- 5+ 7- 11-	2-  2 5+ 7- 11- -2 -3 -7
Curve Equation t 67760br1 [0,-1,0,-2856,191600] 1 67760br2 [0,-1,0,25304,-4719504] 1
67760bs (4 curves)	0	2- 5+ 7- 11-	2-  2 5+ 7- 11- -2  6  2
Curve Equation t 67760bs1 [0,-1,0,-1768576,909705216] 2 67760bs2 [0,-1,0,-28330496,58049707520] 2 67760bs3 [0,-1,0,4397584,4825311680] 2 67760bs4 [0,-1,0,-30295536,49537804736] 2
67760bt (4 curves)	0	2- 5+ 7- 11-	2-  2 5+ 7- 11-  4  0 -4
Curve Equation t 67760bt1 [0,-1,0,-108456,267570800] 2 67760bt2 [0,-1,0,-6923176,6951448176] 2 67760bt3 [0,-1,0,975704,-7207061904] 2 67760bt4 [0,-1,0,-50560616,-134439928720] 2
67760bu (2 curves)	0	2- 5+ 7- 11-	2- -2 5+ 7- 11- -2 -2  6
Curve Equation t 67760bu1 [0,1,0,-6816,-479756] 2 67760bu2 [0,1,0,-142336,-20699340] 2
67760bv (2 curves)	1	2- 5- 7+ 11+	2-  0 5- 7+ 11+  4  0  4
Curve Equation t Generators 67760bv1 [0,0,0,-187,-726] 2 [-10:12:1] 67760bv2 [0,0,0,-1067,12826] 2 [-33:110:1]
67760bw (2 curves)	0	2- 5- 7+ 11-	2-  0 5- 7+ 11- -2  6  4
Curve Equation t 67760bw1 [0,0,0,968,11979] 2 67760bw2 [0,0,0,-5687,114466] 2
67760bx (4 curves)	0	2- 5- 7+ 11-	2-  0 5- 7+ 11- -2 -6  4
Curve Equation t 67760bx1 [0,0,0,-23404667,-52454371926] 2 67760bx2 [0,0,0,-395271547,-3024637597014] 4 67760bx3 [0,0,0,-416141627,-2687489802646] 4 67760bx4 [0,0,0,-6324271547,-193581511797014] 2
67760by (4 curves)	0	2- 5- 7+ 11-	2-  0 5- 7+ 11-  6 -6 -4
Curve Equation t 67760by1 [0,0,0,-71027,9804146] 2 67760by2 [0,0,0,-1242307,532897794] 4 67760by3 [0,0,0,-1348787,436150066] 2 67760by4 [0,0,0,-19876307,34107638994] 4
67760bz (1 curve)	0	2- 5- 7+ 11-	2- -1 5- 7+ 11- -3  0  3
Curve Equation t 67760bz1 [0,-1,0,-637600,-195797248] 1
67760ca (2 curves)	0	2- 5- 7+ 11-	2- -1 5- 7+ 11-  5  0 -5
Curve Equation t 67760ca1 [0,-1,0,-271080,-157187600] 1 67760ca2 [0,-1,0,2390920,3791090800] 1
67760cb (2 curves)	0	2- 5- 7+ 11-	2-  2 5- 7+ 11-  0  0  0
Curve Equation t 67760cb1 [0,-1,0,62880,47302400] 2 67760cb2 [0,-1,0,-1640800,773751552] 2
67760cc (2 curves)	0	2- 5- 7+ 11-	2-  2 5- 7+ 11-  2  3  1
Curve Equation t 67760cc1 [0,-1,0,-40,15600] 1 67760cc2 [0,-1,0,-48440,4119920] 1
67760cd (1 curve)	0	2- 5- 7+ 11-	2-  3 5- 7+ 11-  1  0  7
Curve Equation t 67760cd1 [0,0,0,-187,-25366] 1
67760ce (1 curve)	0	2- 5- 7+ 11-	2- -3 5- 7+ 11- -3 -2  1
Curve Equation t 67760ce1 [0,0,0,-4494787,-3667951166] 1
67760cf (2 curves)	0	2- 5- 7- 11+	2-  0 5- 7- 11+ -4  0 -4
Curve Equation t 67760cf1 [0,0,0,-22627,966306] 2 67760cf2 [0,0,0,-129107,-17071406] 2
67760cg (4 curves)	1	2- 5- 7- 11-	2-  0 5- 7- 11-  6  2 -4
Curve Equation t Generators 67760cg1 [0,0,0,-56507,-54712086] 2 [18223791000855:427201892941824:24973904467] 67760cg2 [0,0,0,-2534587,-1543046934] 4 [-57180:184149:64] 67760cg3 [0,0,0,-4238267,792016874] 4 [-1430:62678:1] 67760cg4 [0,0,0,-40480187,-99131541014] 2 [-115896177380:1629832869:31554496]
67760ch (2 curves)	1	2- 5- 7- 11-	2- -1 5- 7- 11-  1  3  2
Curve Equation t Generators 67760ch1 [0,-1,0,-645,-30743] 1 [49:230:1] 67760ch2 [0,-1,0,-97445,-11675783] 1 [3437:200606:1]
67760ci (1 curve)	1	2- 5- 7- 11-	2- -1 5- 7- 11-  3  0 -3
Curve Equation t Generators 67760ci1 [0,-1,0,-77149640,260914735600] 1 [1170:415030:1]
67760cj (2 curves)	1	2- 5- 7- 11-	2- -1 5- 7- 11- -5  0  5
Curve Equation t Generators 67760cj1 [0,-1,0,-2240,118912] 1 [24:-280:1] 67760cj2 [0,-1,0,19760,-2855488] 1 [904:27440:1]
67760ck (2 curves)	1	2- 5- 7- 11-	2-  2 5- 7- 11- -2 -3 -1
Curve Equation t Generators 67760ck1 [0,-1,0,-4880,-20744128] 1 [9408:119960:27] 67760ck2 [0,-1,0,-5861280,-5460168448] 1 [35016375072:4419693237680:2146689]
67760cl (4 curves)	1	2- 5- 7- 11-	2-  2 5- 7- 11- -2 -6  2
Curve Equation t Generators 67760cl1 [0,-1,0,19320,8441072] 2 [-46:2730:1] 67760cl2 [0,-1,0,-522760,139407600] 2 [2820:145200:1] 67760cl3 [0,-1,0,-174280,-231003408] 2 [7573188:-121687280:9261] 67760cl4 [0,-1,0,-6814760,-6807734800] 2 [3436:101640:1]
67760cm (4 curves)	1	2- 5- 7- 11-	2-  2 5- 7- 11-  4  0 -4
Curve Equation t Generators 67760cm1 [0,-1,0,-300725,-57494248] 2 [-643668:2840005:1728] 67760cm2 [0,-1,0,-1105980,385073900] 2 [3130:27825:8] 67760cm3 [0,-1,0,-23726325,-44475067228] 2 [-261828224516176424124:591465278204940223:93114901321939008] 67760cm4 [0,-1,0,-23732980,-44448862500] 2 [-27192013362:-56272312803:9800344]
67760cn (2 curves)	1	2- 5- 7- 11-	2-  2 5- 7- 11- -4  4 -8
Curve Equation t Generators 67760cn1 [0,-1,0,-40,596400] 2 [1500:58080:1] 67760cn2 [0,-1,0,-106520,13203632] 2 [-326:3630:1]
67760co (2 curves)	1	2- 5- 7- 11-	2- -2 5- 7- 11- -4 -8 -4
Curve Equation t Generators 67760co1 [0,1,0,-10325,397978] 2 [238:3388:1] 67760co2 [0,1,0,-16980,-185000] 2 [183:1694:1]
67760cp (1 curve)	1	2- 5- 7- 11-	2-  3 5- 7- 11- -1  0 -7
Curve Equation t Generators 67760cp1 [0,0,0,-22627,33762146] 1 [12549:300230:27]
67760cq (1 curve)	1	2- 5- 7- 11-	2- -3 5- 7- 11-  3  2 -1
Curve Equation t Generators 67760cq1 [0,0,0,-37147,2755786] 1 [125:256:1]

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