Cremona's table of elliptic curves

56784 = 2⁴ · 3 · 7 · 13²

Class	r	Atkin-Lehner	Eigenvalues
56784a (2 curves)	1	2+ 3+ 7+ 13+	2+ 3+  0 7+ -2 13+ -2  0
Curve Equation t Generators 56784a1 [0,-1,0,87317,7718086] 2 [1031382:-30931642:1331] 56784a2 [0,-1,0,-450948,69941520] 2 [44:7084:1]
56784b (4 curves)	1	2+ 3+ 7+ 13+	2+ 3+ -2 7+  0 13+  6 -4
Curve Equation t Generators 56784b1 [0,-1,0,-1239,17094] 2 [786:1880:27] 56784b2 [0,-1,0,-2084,-8256] 4 [-16:144:1] 56784b3 [0,-1,0,8056,-73152] 2 [22:338:1] 56784b4 [0,-1,0,-25744,-1579280] 2 [5547:35828:27]
56784c (1 curve)	0	2+ 3+ 7+ 13-	2+ 3+ -3 7+  4 13- -6  7
Curve Equation t 56784c1 [0,-1,0,-4697,-175371] 1
56784d (2 curves)	0	2+ 3+ 7- 13+	2+ 3+  0 7- -2 13+ -6 -8
Curve Equation t 56784d1 [0,-1,0,-1744643,-909932310] 2 56784d2 [0,-1,0,-28119628,-57384050192] 2
56784e (6 curves)	0	2+ 3+ 7- 13+	2+ 3+  2 7- -4 13+  2 -4
Curve Equation t 56784e1 [0,-1,0,-40447,-2995838] 2 56784e2 [0,-1,0,-108892,9899200] 4 56784e3 [0,-1,0,286568,64947232] 4 56784e4 [0,-1,0,-1599472,779038480] 4 56784e5 [0,-1,0,-1457512,922815568] 2 56784e6 [0,-1,0,-25590712,49836326032] 2
56784f (4 curves)	0	2+ 3+ 7- 13+	2+ 3+ -2 7-  4 13+  6  4
Curve Equation t 56784f1 [0,-1,0,-6782364,6800865408] 2 56784f2 [0,-1,0,-6785744,6793751184] 4 56784f3 [0,-1,0,-4467064,11505308944] 2 56784f4 [0,-1,0,-9158504,1626829008] 2
56784g (1 curve)	0	2+ 3+ 7- 13+	2+ 3+  3 7- -2 13+  0  7
Curve Equation t 56784g1 [0,-1,0,3831,-114219] 1
56784h (1 curve)	1	2+ 3+ 7- 13-	2+ 3+  3 7- -4 13- -6 -7
Curve Equation t Generators 56784h1 [0,-1,0,-793849,-388465403] 1 [10084:1008423:1]
56784i (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  0 7+ -1 13+  3  1
Curve Equation t 56784i1 [0,1,0,-413768,-102561900] 1
56784j (2 curves)	0	2+ 3- 7+ 13+	2+ 3-  0 7+  2 13+ -2  0
Curve Equation t 56784j1 [0,1,0,-34363,-2446300] 2 56784j2 [0,1,0,-11548,-5622148] 2
56784k (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  2 7+  3 13+ -1  5
Curve Equation t 56784k1 [0,1,0,-6464592,-1566502092] 1
56784l (1 curve)	0	2+ 3- 7+ 13+	2+ 3- -2 7+  0 13+ -3  2
Curve Equation t 56784l1 [0,1,0,8056,-58668] 1
56784m (4 curves)	2	2+ 3- 7+ 13+	2+ 3- -2 7+  0 13+ -6 -4
Curve Equation t Generators 56784m1 [0,1,0,-1239,866100] 2 [44:948:1]&[368:7098:1] 56784m2 [0,1,0,-144044,20744556] 4 [30:4056:1]&[91:2898:1] 56784m3 [0,1,0,-275864,-23283324] 2 [576:3042:1]&[-774:12675:8] 56784m4 [0,1,0,-2297104,1339278500] 4 [1382:-28392:1]&[-1621:28392:1]
56784n (1 curve)	2	2+ 3- 7+ 13+	2+ 3- -2 7+ -3 13+ -3 -7
Curve Equation t Generators 56784n1 [0,1,0,-264,-1260] 1 [-6:-12:1]&[-12:18:1]
56784o (1 curve)	0	2+ 3- 7+ 13+	2+ 3-  3 7+  0 13+  7 -8
Curve Equation t 56784o1 [0,1,0,-54126024,171491539428] 1
56784p (1 curve)	1	2+ 3- 7+ 13-	2+ 3- -3 7+ -5 13-  7  3
Curve Equation t Generators 56784p1 [0,1,0,-44672,-8073324] 1 [24834:729404:27]
56784q (1 curve)	1	2+ 3- 7- 13+	2+ 3-  0 7-  1 13+  3 -1
Curve Equation t Generators 56784q1 [0,1,0,-2448,-47436] 1 [-230:21:8]
56784r (1 curve)	1	2+ 3- 7- 13+	2+ 3- -1 7-  5 13+  3  1
Curve Equation t Generators 56784r1 [0,1,0,-56,-237132] 1 [108:1014:1]
56784s (1 curve)	1	2+ 3- 7- 13+	2+ 3-  2 7-  0 13+ -3 -2
Curve Equation t Generators 56784s1 [0,1,0,48,-12] 1 [14:60:1]
56784t (1 curve)	1	2+ 3- 7- 13+	2+ 3-  2 7-  3 13+ -3  7
Curve Equation t Generators 56784t1 [0,1,0,-44672,-2589612] 1 [-113:1014:1]
56784u (6 curves)	1	2+ 3- 7- 13+	2+ 3-  2 7- -4 13+ -6  4
Curve Equation t Generators 56784u1 [0,1,0,121793,66635492] 2 [9002:322959:8] 56784u2 [0,1,0,-1907052,939850380] 4 [-357:39690:1] 56784u3 [0,1,0,-6378792,-5111308188] 2 [-1033:19410:1] 56784u4 [0,1,0,-29896832,62909223300] 4 [-1400:319410:1] 56784u5 [0,1,0,-29281672,65622571028] 2 [2474:91260:1] 56784u6 [0,1,0,-478348472,4026683578932] 2 [16852:866970:1]
56784v (4 curves)	1	2+ 3- 7- 13+	2+ 3- -2 7-  0 13+ -2  4
Curve Equation t Generators 56784v1 [0,1,0,-1239,-109368] 2 [108:1014:1] 56784v2 [0,1,0,-42644,-3388644] 4 [-125:66:1] 56784v3 [0,1,0,-66304,766052] 2 [-256:1014:1] 56784v4 [0,1,0,-681464,-216754524] 2 [37082:2481765:8]
56784w (1 curve)	1	2+ 3- 7- 13+	2+ 3- -2 7- -3 13+ -1 -5
Curve Equation t Generators 56784w1 [0,1,0,-1092516104,-3437235031788] 1 [259978:-131469156:1]
56784x (4 curves)	1	2+ 3- 7- 13+	2+ 3- -2 7- -4 13+  2  4
Curve Equation t Generators 56784x1 [0,1,0,-15604,-754948] 2 [12702:264880:27] 56784x2 [0,1,0,-18984,-407484] 4 [174:1260:1] 56784x3 [0,1,0,68896,-3043884] 4 [190:4116:1] 56784x4 [0,1,0,-160944,24520692] 2 [33580:107814:125]
56784y (1 curve)	1	2+ 3- 7- 13+	2+ 3-  3 7- -5 13+  3 -1
Curve Equation t Generators 56784y1 [0,1,0,-1742784,889892628] 1 [446:14196:1]
56784z (1 curve)	1	2+ 3- 7- 13+	2+ 3-  3 7-  6 13+ -8 -1
Curve Equation t Generators 56784z1 [0,1,0,-18738635049,-987339457820637] 1 [25036644:14530880091:64]
56784ba (1 curve)	1	2+ 3- 7- 13+	2+ 3- -3 7-  0 13+  7  8
Curve Equation t Generators 56784ba1 [0,1,0,-320272,77958596] 1 [488:-6174:1]
56784bb (2 curves)	1	2+ 3- 7- 13+	2+ 3- -4 7-  6 13+  6 -8
Curve Equation t Generators 56784bb1 [0,1,0,-35715,2585844] 2 [810:1071:8] 56784bb2 [0,1,0,-33180,2971164] 2 [602:14196:1]
56784bc (1 curve)	0	2+ 3- 7- 13-	2+ 3-  3 7-  5 13-  7 -3
Curve Equation t 56784bc1 [0,1,0,-264,-3756] 1
56784bd (2 curves)	0	2- 3+ 7+ 13+	2- 3+  0 7+  3 13+ -3 -5
Curve Equation t 56784bd1 [0,-1,0,-3577448,-2576890512] 1 56784bd2 [0,-1,0,-27305048,53541730800] 1
56784be (2 curves)	2	2- 3+ 7+ 13+	2- 3+  0 7+ -3 13+  3 -5
Curve Equation t Generators 56784be1 [0,-1,0,-1408,2560] 1 [48:208:1]&[-27:142:1] 56784be2 [0,-1,0,-82528,9152896] 1 [360:5096:1]&[18:2770:1]
56784bf (1 curve)	0	2- 3+ 7+ 13+	2- 3+ -1 7+ -2 13+  0  1
Curve Equation t 56784bf1 [0,-1,0,6867259,22253052717] 1
56784bg (1 curve)	0	2- 3+ 7+ 13+	2- 3+ -1 7+ -2 13+ -3 -2
Curve Equation t 56784bg1 [0,-1,0,16844,12432172] 1
56784bh (1 curve)	0	2- 3+ 7+ 13+	2- 3+ -1 7+  3 13+  5  1
Curve Equation t 56784bh1 [0,-1,0,-20336,1289664] 1
56784bi (2 curves)	0	2- 3+ 7+ 13+	2- 3+  2 7+  0 13+ -4 -8
Curve Equation t 56784bi1 [0,-1,0,8563,-519312] 2 56784bi2 [0,-1,0,-68332,-5625140] 2
56784bj (1 curve)	0	2- 3+ 7+ 13+	2- 3+  2 7+  3 13+ -7 -5
Curve Equation t 56784bj1 [0,-1,0,-12347872,-16588583168] 1
56784bk (6 curves)	0	2- 3+ 7+ 13+	2- 3+  2 7+  4 13+ -6  4
Curve Equation t 56784bk1 [0,-1,0,2648,10672] 2 56784bk2 [0,-1,0,-10872,97200] 4 56784bk3 [0,-1,0,-105512,-13076688] 2 56784bk4 [0,-1,0,-132552,18592560] 4 56784bk5 [0,-1,0,-91992,30144048] 2 56784bk6 [0,-1,0,-2119992,1188797232] 2
56784bl (4 curves)	0	2- 3+ 7+ 13+	2- 3+  2 7+ -4 13+ -2 -4
Curve Equation t 56784bl1 [0,-1,0,-152832,22413312] 2 56784bl2 [0,-1,0,-369152,-54942720] 4 56784bl3 [0,-1,0,1091008,-383186688] 2 56784bl4 [0,-1,0,-5290432,-4680945920] 2
56784bm (1 curve)	0	2- 3+ 7+ 13+	2- 3+  2 7+ -4 13+  7  2
Curve Equation t 56784bm1 [0,-1,0,-19712,1072512] 1
56784bn (2 curves)	1	2- 3+ 7+ 13-	2- 3+  0 7+ -4 13- -6  8
Curve Equation t Generators 56784bn1 [0,-1,0,-173,-612] 2 [-8:14:1] 56784bn2 [0,-1,0,412,-4356] 2 [61:494:1]
56784bo (1 curve)	1	2- 3+ 7+ 13-	2- 3+  1 7+  0 13-  2 -5
Curve Equation t Generators 56784bo1 [0,-1,0,35,-287] 1 [9:-26:1]
56784bp (1 curve)	1	2- 3+ 7+ 13-	2- 3+ -1 7+  3 13- -7 -3
Curve Equation t Generators 56784bp1 [0,-1,0,-742096,-266048576] 1 [38624850:1781460278:15625]
56784bq (4 curves)	1	2- 3+ 7+ 13-	2- 3+ -2 7+  0 13-  2  4
Curve Equation t Generators 56784bq1 [0,-1,0,-1222264,519860080] 2 [17940:21520:27] 56784bq2 [0,-1,0,-870744,824698224] 2 [948:29160:1] 56784bq3 [0,-1,0,-36550024,-85008330512] 2 [41020440972597373404:7311094279349567253760:1244759982330411] 56784bq4 [0,-1,0,-30925704,-112068058896] 2 [1592952492:575847954720:12167]
56784br (2 curves)	1	2- 3+ 7+ 13-	2- 3+  3 7+  0 13-  2 -1
Curve Equation t Generators 56784br1 [0,-1,0,128891,-203126483] 1 [2579240149180:365051422297809:128787625] 56784br2 [0,-1,0,-173873509,-882408581939] 1 [7760613660477556704860768908117419347910797501089340:867037586994947497960518894084898060287903318679879017:350560803519590390688221571317731678601213926625]
56784bs (2 curves)	1	2- 3+ 7+ 13-	2- 3+  3 7+  5 13- -3 -1
Curve Equation t Generators 56784bs1 [0,-1,0,-188504,31564272] 1 [204:1248:1] 56784bs2 [0,-1,0,388696,162788976] 1 [297540:162299904:1]
56784bt (2 curves)	1	2- 3+ 7+ 13-	2- 3+ -4 7+  0 13-  2  0
Curve Equation t Generators 56784bt1 [0,-1,0,-86098965,307528130376] 2 [23266948:-379668758:4913] 56784bt2 [0,-1,0,-85209180,314194399596] 2 [1855173046427582:-41904866422769917:369219064024]
56784bu (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7-  3 13+  3  5
Curve Equation t Generators 56784bu1 [0,-1,0,-238008,4672368] 1 [34979:12756080:6859] 56784bu2 [0,-1,0,-13947288,20053123440] 1 [2153:112:1]
56784bv (2 curves)	1	2- 3+ 7- 13+	2- 3+  0 7- -3 13+ -3  5
Curve Equation t Generators 56784bv1 [0,-1,0,-21168,-1166400] 1 [200:1600:1] 56784bv2 [0,-1,0,-161568,24420096] 1 [1520:57344:1]
56784bw (4 curves)	1	2- 3+ 7- 13+	2- 3+  0 7- -6 13+  0 -4
Curve Equation t Generators 56784bw1 [0,-1,0,1127,4588] 2 [618:5915:8] 56784bw2 [0,-1,0,-4788,42444] 2 [-15813:138510:343] 56784bw3 [0,-1,0,-19153,1057120] 2 [204:2366:1] 56784bw4 [0,-1,0,-308988,66212028] 2 [309:378:1]
56784bx (1 curve)	1	2- 3+ 7- 13+	2- 3+  1 7-  2 13+ -3  2
Curve Equation t Generators 56784bx1 [0,-1,0,100,5628] 1 [-38:567:8]
56784by (2 curves)	1	2- 3+ 7- 13+	2- 3+  1 7-  5 13+ -3 -1
Curve Equation t Generators 56784by1 [0,-1,0,1930600,11665250544] 1 [-1460:75712:1] 56784by2 [0,-1,0,-9935837240,381205001294064] 1 [72232556:1796914808:1331]
56784bz (1 curve)	1	2- 3+ 7- 13+	2- 3+ -2 7- -3 13+ -7  5
Curve Equation t Generators 56784bz1 [0,-1,0,-73064,-7528080] 1 [-1174:883:8]
56784ca (1 curve)	1	2- 3+ 7- 13+	2- 3+ -2 7-  4 13+  7 -2
Curve Equation t Generators 56784ca1 [0,-1,0,-3331384,2342983408] 1 [-732:66248:1]
56784cb (4 curves)	1	2- 3+ 7- 13+	2- 3+ -2 7- -4 13+  6 -4
Curve Equation t Generators 56784cb1 [0,-1,0,-18984,908400] 2 [-134:1014:1] 56784cb2 [0,-1,0,-73064,-6619536] 4 [-124:720:1] 56784cb3 [0,-1,0,116216,-35390096] 2 [2242:107190:1] 56784cb4 [0,-1,0,-1127624,-460502160] 2 [1660:47320:1]
56784cc (3 curves)	1	2- 3+ 7- 13+	2- 3+ -3 7-  3 13+ -3 -7
Curve Equation t Generators 56784cc1 [0,-1,0,36448,-25479936] 1 [490:10478:1] 56784cc2 [0,-1,0,-328592,694378944] 1 [802:30758:1] 56784cc3 [0,-1,0,-70456832,227658891264] 1 [4858:2366:1]
56784cd (2 curves)	0	2- 3+ 7- 13-	2- 3+  0 7-  4 13- -6 -8
Curve Equation t 56784cd1 [0,-1,0,-29293,-1461656] 2 56784cd2 [0,-1,0,69572,-9291764] 2
56784ce (1 curve)	0	2- 3+ 7- 13-	2- 3+  1 7- -3 13- -7  3
Curve Equation t 56784ce1 [0,-1,0,-125414280,-585010378512] 1
56784cf (1 curve)	0	2- 3+ 7- 13-	2- 3+ -1 7-  0 13-  2  5
Curve Equation t 56784cf1 [0,-1,0,5859,-607023] 1
56784cg (4 curves)	0	2- 3+ 7- 13-	2- 3+  2 7-  0 13-  2 -4
Curve Equation t 56784cg1 [0,-1,0,-7232,238848] 2 56784cg2 [0,-1,0,-5152,376960] 2 56784cg3 [0,-1,0,-216272,-38626368] 2 56784cg4 [0,-1,0,-182992,-50953280] 2
56784ch (2 curves)	0	2- 3+ 7- 13-	2- 3+ -3 7-  0 13-  2  1
Curve Equation t 56784ch1 [0,-1,0,763,-92691] 1 56784ch2 [0,-1,0,-1028837,-401325939] 1
56784ci (2 curves)	0	2- 3+ 7- 13-	2- 3+ -3 7- -5 13- -3  1
Curve Equation t 56784ci1 [0,-1,0,-31857232,69219276736] 1 56784ci2 [0,-1,0,65689568,357910138624] 1
56784cj (2 curves)	0	2- 3+ 7- 13-	2- 3+  4 7-  0 13-  2  0
Curve Equation t 56784cj1 [0,-1,0,-509461,140133148] 2 56784cj2 [0,-1,0,-504196,143165788] 2
56784ck (2 curves)	1	2- 3- 7+ 13+	2- 3-  0 7+ -2 13+  4  4
Curve Equation t Generators 56784ck1 [0,1,0,-52953,-9116730] 2 [38070:220038:125] 56784ck2 [0,1,0,-1052588,-415768248] 2 [14035810:1658347821:1000]
56784cl (1 curve)	1	2- 3- 7+ 13+	2- 3-  1 7+ -1 13+ -1  7
Curve Equation t Generators 56784cl1 [0,1,0,-293440,61889972] 1 [212:3042:1]
56784cm (1 curve)	1	2- 3- 7+ 13+	2- 3-  1 7+  2 13+ -4  1
Curve Equation t Generators 56784cm1 [0,1,0,-334845,-187376409] 1 [975:20346:1]
56784cn (6 curves)	1	2- 3- 7+ 13+	2- 3-  2 7+ -4 13+  2 -4
Curve Equation t Generators 56784cn1 [0,1,0,-10872,-967212] 2 [3985578:67445760:12167] 56784cn2 [0,1,0,-227192,-41721900] 4 [1318:44160:1] 56784cn3 [0,1,0,-281272,-20414380] 4 [-412:5070:1] 56784cn4 [0,1,0,-3634232,-2667868332] 2 [17642:54855:8] 56784cn5 [0,1,0,1043688,-156620268] 2 [654:-28392:1] 56784cn6 [0,1,0,-2471512,1480338068] 2 [5204:359970:1]
56784co (1 curve)	1	2- 3- 7+ 13+	2- 3- -2 7+  0 13+  1 -6
Curve Equation t Generators 56784co1 [0,1,0,-18984,-1405260] 1 [174:768:1]
56784cp (1 curve)	1	2- 3- 7+ 13+	2- 3- -2 7+ -1 13+ -1  1
Curve Equation t Generators 56784cp1 [0,1,0,-784,-4588] 1 [34:96:1]
56784cq (1 curve)	1	2- 3- 7+ 13+	2- 3- -3 7+  1 13+  7  1
Curve Equation t Generators 56784cq1 [0,1,0,-271708792,1733637352916] 1 [15110:1038336:1]
56784cr (1 curve)	1	2- 3- 7+ 13+	2- 3- -3 7+  4 13+ -5  4
Curve Equation t Generators 56784cr1 [0,1,0,-1512,-42444] 1 [60:294:1]
56784cs (1 curve)	1	2- 3- 7+ 13+	2- 3-  4 7+  3 13+ -5 -3
Curve Equation t Generators 56784cs1 [0,1,0,-1960456,-740711308] 1 [-877:17460:1]
56784ct (2 curves)	1	2- 3- 7+ 13+	2- 3- -4 7+  2 13+ -4 -4
Curve Equation t Generators 56784ct1 [0,1,0,-225,5214] 2 [58:507:8] 56784ct2 [0,1,0,-6140,182664] 2 [-65:558:1]
56784cu (1 curve)	0	2- 3- 7+ 13-	2- 3-  1 7+  1 13- -1  1
Curve Equation t 56784cu1 [0,1,0,254120,-1042924] 1
56784cv (2 curves)	0	2- 3- 7+ 13-	2- 3- -2 7+ -2 13-  2  4
Curve Equation t 56784cv1 [0,1,0,-16172849,-16171749450] 2 56784cv2 [0,1,0,-232390604,-1363381337304] 2
56784cw (1 curve)	0	2- 3- 7- 13+	2- 3-  1 7- -2 13+ -4  3
Curve Equation t 56784cw1 [0,1,0,-71205,-8391213] 1
56784cx (1 curve)	2	2- 3- 7- 13+	2- 3- -1 7- -6 13+ -8  3
Curve Equation t Generators 56784cx1 [0,1,0,-61741,6027191] 1 [-217:3042:1]&[-73:3186:1]
56784cy (1 curve)	0	2- 3- 7- 13+	2- 3-  2 7-  0 13+  1  6
Curve Equation t 56784cy1 [0,1,0,-3208352,-3074522892] 1
56784cz (2 curves)	0	2- 3- 7- 13+	2- 3-  2 7-  0 13+  4  0
Curve Equation t 56784cz1 [0,1,0,-4957,-151618] 2 56784cz2 [0,1,0,-81852,-9040680] 2
56784da (1 curve)	0	2- 3- 7- 13+	2- 3-  2 7-  1 13+ -1 -1
Curve Equation t 56784da1 [0,1,0,-132552,-9549708] 1
56784db (1 curve)	0	2- 3- 7- 13+	2- 3-  3 7- -4 13+ -5 -4
Curve Equation t 56784db1 [0,1,0,-255584,-92227212] 1
56784dc (1 curve)	2	2- 3- 7- 13+	2- 3- -4 7- -3 13+ -5  3
Curve Equation t Generators 56784dc1 [0,1,0,-11600,-340716] 1 [-86:168:1]&[-65:378:1]
56784dd (1 curve)	1	2- 3- 7- 13-	2- 3- -1 7- -1 13- -1 -1
Curve Equation t Generators 56784dd1 [0,1,0,1504,-12] 1 [4:78:1]
56784de (2 curves)	1	2- 3- 7- 13-	2- 3-  2 7-  2 13-  2 -4
Curve Equation t Generators 56784de1 [0,1,0,-95697,-7390278] 2 [-126:1638:1] 56784de2 [0,1,0,-1375092,-620988120] 2 [1863:57330:1]

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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