Cremona's table of elliptic curves

75504 = 2⁴ · 3 · 11² · 13

Class	r	Atkin-Lehner	Eigenvalues
75504a (4 curves)	0	2+ 3+ 11- 13+	2+ 3+  2  0 11- 13+ -2 -4
Curve Equation t 75504a1 [0,-1,0,-887,6162] 2 75504a2 [0,-1,0,-6332,-187680] 4 75504a3 [0,-1,0,928,-600048] 2 75504a4 [0,-1,0,-100712,-12268320] 2
75504b (2 curves)	0	2+ 3+ 11- 13+	2+ 3+  2  0 11- 13+ -8  2
Curve Equation t 75504b1 [0,-1,0,717248,395792080] 2 75504b2 [0,-1,0,-5724792,4333166928] 2
75504c (4 curves)	0	2+ 3+ 11- 13+	2+ 3+  2  4 11- 13+  6  0
Curve Equation t 75504c1 [0,-1,0,-92847,8013942] 2 75504c2 [0,-1,0,-533892,-143529120] 4 75504c3 [0,-1,0,315528,-558046080] 2 75504c4 [0,-1,0,-8440032,-9434824848] 2
75504d (2 curves)	1	2+ 3+ 11- 13-	2+ 3+  0  0 11- 13- -2  0
Curve Equation t Generators 75504d1 [0,-1,0,-403,-6422] 2 [250614:2617022:2197] 75504d2 [0,-1,0,-8268,-286416] 2 [456:9516:1]
75504e (2 curves)	1	2+ 3+ 11- 13-	2+ 3+  0  0 11- 13-  4  0
Curve Equation t Generators 75504e1 [0,-1,0,345052,-284361504] 2 [10239704818608726777:-283512885773996959278:12997931998676561] 75504e2 [0,-1,0,-4947488,-3895990800] 2 [-9977447686:-110251444886:6967871]
75504f (2 curves)	1	2+ 3+ 11- 13-	2+ 3+  2  4 11- 13- -4 -2
Curve Equation t Generators 75504f1 [0,-1,0,10608,-42480] 2 [17895:465850:27] 75504f2 [0,-1,0,-42632,-298032] 2 [2666:137214:1]
75504g (4 curves)	1	2+ 3+ 11- 13-	2+ 3+ -2  0 11- 13-  2 -4
Curve Equation t Generators 75504g1 [0,-1,0,4316,-17312] 2 [328:6048:1] 75504g2 [0,-1,0,-17464,-121856] 4 [-106:726:1] 75504g3 [0,-1,0,-177184,28627744] 4 [1346:47190:1] 75504g4 [0,-1,0,-206224,-35910752] 2 [-262:258:1]
75504h (1 curve)	1	2+ 3+ 11- 13-	2+ 3+ -3  3 11- 13-  4  6
Curve Equation t Generators 75504h1 [0,-1,0,20288,-272864] 1 [37:726:1]
75504i (2 curves)	1	2+ 3+ 11- 13-	2+ 3+ -4 -4 11- 13-  6  4
Curve Equation t Generators 75504i1 [0,-1,0,565,16326] 2 [-14:74:1] 75504i2 [0,-1,0,-7300,220816] 2 [-84:484:1]
75504j (2 curves)	0	2+ 3- 11+ 13+	2+ 3-  0  0 11+ 13+  2  2
Curve Equation t 75504j1 [0,1,0,-1888,-32188] 2 75504j2 [0,1,0,-2328,-16524] 2
75504k (1 curve)	0	2+ 3- 11+ 13+	2+ 3-  3  1 11+ 13+  6 -2
Curve Equation t 75504k1 [0,1,0,-36824,-4390476] 1
75504l (2 curves)	0	2+ 3- 11+ 13+	2+ 3-  4  0 11+ 13+  0  4
Curve Equation t 75504l1 [0,1,0,-216,-2268] 2 75504l2 [0,1,0,-4176,-105228] 2
75504m (2 curves)	1	2+ 3- 11+ 13-	2+ 3-  0  0 11+ 13- -2 -2
Curve Equation t Generators 75504m1 [0,1,0,-228488,41928324] 2 [318:1236:1] 75504m2 [0,1,0,-281728,20866580] 2 [-58:6084:1]
75504n (1 curve)	1	2+ 3- 11+ 13-	2+ 3-  3 -1 11+ 13- -6  2
Curve Equation t Generators 75504n1 [0,1,0,-304,3188] 1 [-4:66:1]
75504o (2 curves)	1	2+ 3- 11+ 13-	2+ 3-  4  0 11+ 13-  0 -4
Curve Equation t Generators 75504o1 [0,1,0,-26176,2914052] 2 [98:1140:1] 75504o2 [0,1,0,-505336,138037172] 2 [52180:9234:125]
75504p (1 curve)	1	2+ 3- 11- 13+	2+ 3- -1  3 11- 13+  0 -6
Curve Equation t Generators 75504p1 [0,1,0,-587616,-205242732] 1 [1668:-58806:1]
75504q (1 curve)	1	2+ 3- 11- 13+	2+ 3-  2 -3 11- 13+  0 -3
Curve Equation t Generators 75504q1 [0,1,0,331863,466108707] 1 [3353769983947136974:180840262342297782003:6493778947969496]
75504r (6 curves)	1	2+ 3- 11- 13+	2+ 3- -2  0 11- 13+ -2  4
Curve Equation t Generators 75504r1 [0,1,0,-571039,165901052] 2 [5452012:5370480:12167] 75504r2 [0,1,0,-571644,165531276] 4 [714:11040:1] 75504r3 [0,1,0,-288504,329865732] 2 [65655:2248296:125] 75504r4 [0,1,0,-864464,-22459164] 4 [-410:16224:1] 75504r5 [0,1,0,3447976,-175982028] 2 [1987:120516:1] 75504r6 [0,1,0,-9862024,-11895639340] 2 [8807:764478:1]
75504s (4 curves)	1	2+ 3- 11- 13+	2+ 3- -2  4 11- 13+ -2  8
Curve Equation t Generators 75504s1 [0,1,0,-4759,124760] 2 [26276:525987:64] 75504s2 [0,1,0,-5364,90396] 4 [66:168:1] 75504s3 [0,1,0,16416,656676] 2 [-198:3885:8] 75504s4 [0,1,0,-36824,-2665500] 2 [-98:108:1]
75504t (1 curve)	1	2+ 3- 11- 13+	2+ 3-  4 -3 11- 13+ -2  1
Curve Equation t Generators 75504t1 [0,1,0,-19521,-2988933] 1 [10456710332007730:4760711906837744013:50447927375]
75504u (2 curves)	0	2+ 3- 11- 13-	2+ 3-  0  4 11- 13- -8  4
Curve Equation t 75504u1 [0,1,0,1412,-329716] 2 75504u2 [0,1,0,-63928,-6053500] 2
75504v (2 curves)	0	2+ 3- 11- 13-	2+ 3-  0 -4 11- 13-  6 -4
Curve Equation t 75504v1 [0,1,0,-403,-1564] 2 75504v2 [0,1,0,1412,-10276] 2
75504w (1 curve)	0	2+ 3- 11- 13-	2+ 3-  2  3 11- 13-  0  3
Curve Equation t 75504w1 [0,1,0,2743,-349197] 1
75504x (2 curves)	0	2+ 3- 11- 13-	2+ 3-  4  0 11- 13- -2  8
Curve Equation t 75504x1 [0,1,0,-78811,7974272] 2 75504x2 [0,1,0,68204,34436972] 2
75504y (1 curve)	0	2+ 3- 11- 13-	2+ 3-  4  3 11- 13-  2 -1
Curve Equation t 75504y1 [0,1,0,-161,2187] 1
75504z (2 curves)	0	2- 3+ 11+ 13+	2- 3+  0  0 11+ 13+  0  0
Curve Equation t 75504z1 [0,-1,0,37712,1574080] 2 75504z2 [0,-1,0,-175248,13670208] 2
75504ba (1 curve)	0	2- 3+ 11+ 13+	2- 3+ -3  3 11+ 13+  6  6
Curve Equation t 75504ba1 [0,-1,0,-83552,-15055104] 1
75504bb (2 curves)	1	2- 3+ 11+ 13-	2- 3+  0  0 11+ 13-  0  0
Curve Equation t Generators 75504bb1 [0,-1,0,312,-1296] 2 [20:112:1] 75504bb2 [0,-1,0,-1448,-9744] 2 [-20:104:1]
75504bc (1 curve)	1	2- 3+ 11+ 13-	2- 3+ -3 -3 11+ 13- -6 -6
Curve Equation t Generators 75504bc1 [0,-1,0,-10109832,20078782704] 1 [4074:215622:1]
75504bd (2 curves)	1	2- 3+ 11- 13+	2- 3+  0 -1 11- 13+  0 -1
Curve Equation t Generators 75504bd1 [0,-1,0,-510253,140564833] 1 [141:8450:1] 75504bd2 [0,-1,0,558947,616316065] 1 [1862301585:85193178850:1442897]
75504be (2 curves)	1	2- 3+ 11- 13+	2- 3+  0 -1 11- 13+ -6 -1
Curve Equation t Generators 75504be1 [0,-1,0,-1173,16029] 1 [20:13:1] 75504be2 [0,-1,0,4107,78333] 1 [7780:94471:125]
75504bf (4 curves)	1	2- 3+ 11- 13+	2- 3+  0  2 11- 13+  6  2
Curve Equation t Generators 75504bf1 [0,-1,0,-1613,1080] 2 [114296:516456:2197] 75504bf2 [0,-1,0,-17948,928908] 2 [1659:6292:27] 75504bf3 [0,-1,0,-88733,-10144044] 2 [-87377165985937800:-2181822131187413:508169592000000] 75504bf4 [0,-1,0,-90548,-9705540] 2 [-87947925:-109625516:421875]
75504bg (4 curves)	1	2- 3+ 11- 13+	2- 3+  0  2 11- 13+ -6  2
Curve Equation t Generators 75504bg1 [0,-1,0,-11515973,-14811606984] 2 [-6712745278601507750435242314924431295413604:-49279506662678428806686018392085070231958431:3354561032245587865016443070421254595008] 75504bg2 [0,-1,0,-23424188,21074989740] 2 [-21532822214785467136811:-1066006774943400508045894:5076396130596048721] 75504bg3 [0,-1,0,-928889573,-10896371582556] 2 [-243079325405487199436198097065567050908483179498723883293600544202296188805675716525043276757893397444187602479345337900729651671540:71905382247172565359457853918467570275240083689677353619966137001414938174084654214184097871246687551268808217537741410834480037:13814505800768027271548130111238885338322049361950364073473678602827912274450962172330889922516621227668617161996184409181944000] 75504bg4 [0,-1,0,-928905908,-10895969166564] 2 [-275088674791755633190440532143048517665179013918295306159461824458:375819839606157296778949135382494403097354273772042655028216863345:15593236954881320990517243327538250638499551747664357345714744]
75504bh (4 curves)	1	2- 3+ 11- 13+	2- 3+  0 -4 11- 13+  0 -4
Curve Equation t Generators 75504bh1 [0,-1,0,695952,160449984] 2 [5130:372438:1] 75504bh2 [0,-1,0,-3485808,1428359616] 2 [142734:9761554:27] 75504bh3 [0,-1,0,-7231968,-9993629952] 2 [85904850:5330870622:15625] 75504bh4 [0,-1,0,-126179808,-545449226496] 2 [790318731836550:-60430475659192694:49633171875]
75504bi (1 curve)	1	2- 3+ 11- 13+	2- 3+  2  2 11- 13+  4  3
Curve Equation t Generators 75504bi1 [0,-1,0,928,-385152] 1 [136:1496:1]
75504bj (6 curves)	1	2- 3+ 11- 13+	2- 3+ -2  0 11- 13+  6 -4
Curve Equation t Generators 75504bj1 [0,-1,0,-46504,5552560] 2 [-172:2904:1] 75504bj2 [0,-1,0,-830584,291584944] 4 [-116:19656:1] 75504bj3 [0,-1,0,-917704,226767664] 4 [-3858:508690:27] 75504bj4 [0,-1,0,-13288744,18649929520] 2 [2546:36246:1] 75504bj5 [0,-1,0,2596136,1542349360] 2 [3364873410:-208797760990:2146689] 75504bj6 [0,-1,0,-5825464,-5238513872] 2 [-4010610:7216174:3375]
75504bk (1 curve)	1	2- 3+ 11- 13+	2- 3+ -2 -2 11- 13+  0 -1
Curve Equation t Generators 75504bk1 [0,-1,0,-1184,16128] 1 [16:32:1]
75504bl (2 curves)	1	2- 3+ 11- 13+	2- 3+ -2 -2 11- 13+  0  2
Curve Equation t Generators 75504bl1 [0,-1,0,-13229,24165264] 2 [2512:125840:1] 75504bl2 [0,-1,0,-1336364,588350028] 2 [62045:857648:125]
75504bm (1 curve)	1	2- 3+ 11- 13+	2- 3+ -2  3 11- 13+  0 -1
Curve Equation t Generators 75504bm1 [0,-1,0,-18949,-997907] 1 [3309438:51109721:10648]
75504bn (2 curves)	1	2- 3+ 11- 13+	2- 3+ -2  4 11- 13+  0  2
Curve Equation t Generators 75504bn1 [0,-1,0,-12624,-780096] 2 [115255:1964556:343] 75504bn2 [0,-1,0,-225584,-41157312] 2 [1346:45738:1]
75504bo (1 curve)	1	2- 3+ 11- 13+	2- 3+ -2 -5 11- 13+ -2 -5
Curve Equation t Generators 75504bo1 [0,-1,0,49691,5347465] 1 [81:-3146:1]
75504bp (2 curves)	1	2- 3+ 11- 13+	2- 3+  3 -1 11- 13+  0  2
Curve Equation t Generators 75504bp1 [0,-1,0,-201317904,1099508354496] 1 [8280:13824:1] 75504bp2 [0,-1,0,-156276864,1604393496576] 1 [-1999680:12582912:125]
75504bq (2 curves)	1	2- 3+ 11- 13+	2- 3+ -3  5 11- 13+  0  2
Curve Equation t Generators 75504bq1 [0,-1,0,25128,-3422736] 1 [873:26136:1] 75504bq2 [0,-1,0,-1194552,-503003664] 1 [439887:2924328:343]
75504br (2 curves)	0	2- 3+ 11- 13-	2- 3+  0  1 11- 13-  0  1
Curve Equation t 75504br1 [0,-1,0,-61740653,-186844830159] 1 75504br2 [0,-1,0,67632547,-820587212751] 1
75504bs (2 curves)	0	2- 3+ 11- 13-	2- 3+  0  1 11- 13-  6  1
Curve Equation t 75504bs1 [0,-1,0,-141973,-20766755] 1 75504bs2 [0,-1,0,496907,-106248899] 1
75504bt (2 curves)	0	2- 3+ 11- 13-	2- 3+ -1  1 11- 13- -4  6
Curve Equation t 75504bt1 [0,-1,0,-11179240376,455440355271024] 1 75504bt2 [0,-1,0,31659580264,-28583022592376976] 1
75504bu (1 curve)	0	2- 3+ 11- 13-	2- 3+  2 -2 11- 13- -4 -3
Curve Equation t 75504bu1 [0,-1,0,112248,512188272] 1
75504bv (2 curves)	0	2- 3+ 11- 13-	2- 3+  2  4 11- 13-  8 -6
Curve Equation t 75504bv1 [0,-1,0,-642792,-508532880] 2 75504bv2 [0,-1,0,-14272232,-20723718288] 2
75504bw (1 curve)	0	2- 3+ 11- 13-	2- 3+ -2  2 11- 13-  0  1
Curve Equation t 75504bw1 [0,-1,0,-143304,-20893200] 1
75504bx (1 curve)	0	2- 3+ 11- 13-	2- 3+ -2 -3 11- 13-  0  1
Curve Equation t 75504bx1 [0,-1,0,-2292869,1337385645] 1
75504by (1 curve)	0	2- 3+ 11- 13-	2- 3+ -2  5 11- 13-  2  5
Curve Equation t 75504by1 [0,-1,0,411,-4167] 1
75504bz (2 curves)	0	2- 3+ 11- 13-	2- 3+  4 -4 11- 13- -4 -4
Curve Equation t 75504bz1 [0,-1,0,-1976,-588432] 2 75504bz2 [0,-1,0,-118136,-15456912] 2
75504ca (2 curves)	1	2- 3- 11+ 13+	2- 3-  0  0 11+ 13+  4  4
Curve Equation t Generators 75504ca1 [0,1,0,753152,663874484] 2 [-532:10626:1] 75504ca2 [0,1,0,-8370688,8295054260] 2 [27116:4440702:1]
75504cb (1 curve)	1	2- 3- 11+ 13+	2- 3- -3  3 11+ 13+ -2 -2
Curve Equation t Generators 75504cb1 [0,1,0,-410912,101317236] 1 [898:21384:1]
75504cc (2 curves)	1	2- 3- 11+ 13+	2- 3-  4 -4 11+ 13+ -2 -2
Curve Equation t Generators 75504cc1 [0,1,0,-3859456,-2356150348] 2 [-3555091584713814:-57943820009553920:2716456674177] 75504cc2 [0,1,0,-58377216,-171688312908] 2 [-9172163231107556531639387115:-5484404084266634246506588438:2084384469386129021350875]
75504cd (2 curves)	0	2- 3- 11+ 13-	2- 3-  0  0 11+ 13- -4 -4
Curve Equation t 75504cd1 [0,1,0,91131352,-883252412748] 2 75504cd2 [0,1,0,-1012853288,-11044768633164] 2
75504ce (1 curve)	0	2- 3- 11+ 13-	2- 3- -3 -3 11+ 13-  2  2
Curve Equation t 75504ce1 [0,1,0,-49720392,-135052122636] 1
75504cf (2 curves)	0	2- 3- 11+ 13-	2- 3-  4  4 11+ 13-  2  2
Curve Equation t 75504cf1 [0,1,0,-31896,1758612] 2 75504cf2 [0,1,0,-482456,128816532] 2
75504cg (2 curves)	0	2- 3- 11- 13+	2- 3-  0  0 11- 13+  4 -8
Curve Equation t 75504cg1 [0,1,0,3832,116532] 2 75504cg2 [0,1,0,-25208,1150356] 2
75504ch (1 curve)	0	2- 3- 11- 13+	2- 3-  0  1 11- 13+  2 -3
Curve Equation t 75504ch1 [0,1,0,-780853,-6111155569] 1
75504ci (2 curves)	0	2- 3- 11- 13+	2- 3-  0 -2 11- 13+  2  6
Curve Equation t 75504ci1 [0,1,0,-64533,6282450] 2 75504ci2 [0,1,0,-80868,2839032] 2
75504cj (1 curve)	0	2- 3- 11- 13+	2- 3-  0 -3 11- 13+ -8  1
Curve Equation t 75504cj1 [0,1,0,-1952133,-1676630925] 1
75504ck (1 curve)	0	2- 3- 11- 13+	2- 3-  2  2 11- 13+ -4  7
Curve Equation t 75504ck1 [0,1,0,-100712,65630772] 1
75504cl (1 curve)	0	2- 3- 11- 13+	2- 3-  2 -3 11- 13+  2 -7
Curve Equation t 75504cl1 [0,1,0,-14197,-1210717] 1
75504cm (4 curves)	0	2- 3- 11- 13+	2- 3-  2  4 11- 13+ -2 -8
Curve Equation t 75504cm1 [0,1,0,-37792,59025140] 2 75504cm2 [0,1,0,-2515872,1521092340] 4 75504cm3 [0,1,0,-4529312,-1259870988] 2 75504cm4 [0,1,0,-40151712,97914005748] 2
75504cn (4 curves)	0	2- 3- 11- 13+	2- 3-  2 -4 11- 13+ -2  0
Curve Equation t 75504cn1 [0,1,0,928,-22860] 2 75504cn2 [0,1,0,-8752,-274540] 4 75504cn3 [0,1,0,-37792,2548148] 2 75504cn4 [0,1,0,-134592,-19049868] 2
75504co (1 curve)	0	2- 3- 11- 13+	2- 3-  2  5 11- 13+  2  1
Curve Equation t 75504co1 [0,1,0,-6306197,6093259203] 1
75504cp (4 curves)	2	2- 3- 11- 13+	2- 3- -2  0 11- 13+ -6  0
Curve Equation t Generators 75504cp1 [0,1,0,-298184,72762996] 2 [-290:11616:1]&[-66:9600:1] 75504cp2 [0,1,0,-4983304,4280000756] 4 [-628:84630:1]&[-290:75504:1] 75504cp3 [0,1,0,-5196264,3894032052] 2 [2262:-60984:1]&[-2346:56376:1] 75504cp4 [0,1,0,-79732264,274004148020] 2 [5159:498:1]&[6244:140118:1]
75504cq (1 curve)	2	2- 3- 11- 13+	2- 3- -2 -3 11- 13+  0 -3
Curve Equation t Generators 75504cq1 [0,1,0,-29,-585] 1 [19:-78:1]&[27:138:1]
75504cr (1 curve)	0	2- 3- 11- 13+	2- 3- -3  1 11- 13+  8 -6
Curve Equation t 75504cr1 [0,1,0,-1107432,10130011956] 1
75504cs (2 curves)	0	2- 3- 11- 13+	2- 3-  4  0 11- 13+  0  0
Curve Equation t 75504cs1 [0,1,0,-4454776,-3636291628] 2 75504cs2 [0,1,0,-71362936,-232060749868] 2
75504ct (2 curves)	0	2- 3- 11- 13+	2- 3- -4 -2 11- 13+ -2 -2
Curve Equation t 75504ct1 [0,1,0,-645,5454] 2 75504ct2 [0,1,0,-2460,-41736] 2
75504cu (1 curve)	1	2- 3- 11- 13-	2- 3-  0 -1 11- 13- -2  3
Curve Equation t Generators 75504cu1 [0,1,0,-6453,4589055] 1 [27:-2106:1]
75504cv (1 curve)	1	2- 3- 11- 13-	2- 3-  0  3 11- 13-  8 -1
Curve Equation t Generators 75504cv1 [0,1,0,-16133,1253811] 1 [-26:1287:1]
75504cw (1 curve)	1	2- 3- 11- 13-	2- 3- -1 -3 11- 13-  4 -2
Curve Equation t Generators 75504cw1 [0,1,0,-89096,10733556] 1 [172:-726:1]
75504cx (4 curves)	1	2- 3- 11- 13-	2- 3-  2  0 11- 13- -2  4
Curve Equation t Generators 75504cx1 [0,1,0,10608,-9396972] 2 [93185640:3560470389:64000] 75504cx2 [0,1,0,-608912,-178154220] 4 [374404:28370265:64] 75504cx3 [0,1,0,-1460752,429378068] 4 [44:19110:1] 75504cx4 [0,1,0,-9669392,-11576238060] 2 [-5472808805:-285384036:3048625]
75504cy (1 curve)	1	2- 3- 11- 13-	2- 3-  2 -2 11- 13-  4 -7
Curve Equation t Generators 75504cy1 [0,1,0,-832,-49612] 1 [122:1296:1]
75504cz (1 curve)	1	2- 3- 11- 13-	2- 3-  2  3 11- 13- -2  7
Curve Equation t Generators 75504cz1 [0,1,0,-117,867] 1 [138:559:27]
75504da (4 curves)	1	2- 3- 11- 13-	2- 3-  2  4 11- 13- -2 -4
Curve Equation t Generators 75504da1 [0,1,0,-2065752,1140587028] 2 [1932:66066:1] 75504da2 [0,1,0,-2685272,399393300] 4 [-92:25410:1] 75504da3 [0,1,0,10402088,3158208788] 2 [-58:50544:1] 75504da4 [0,1,0,-25684952,-49785908460] 2 [-359980:2190342:125]
75504db (1 curve)	1	2- 3- 11- 13-	2- 3-  2 -5 11- 13- -2 -1
Curve Equation t Generators 75504db1 [0,1,0,-763049877,-8113180198653] 1 [2658689670110252286:256060795280532286707:73081817638129]
75504dc (1 curve)	1	2- 3- 11- 13-	2- 3- -2  3 11- 13-  0  3
Curve Equation t Generators 75504dc1 [0,1,0,-3549,764487] 1 [-81:726:1]

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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