Cremona's table of elliptic curves

51744 = 2⁵ · 3 · 7² · 11

Class	r	Atkin-Lehner	Eigenvalues
51744a (1 curve)	1	2+ 3+ 7+ 11+	2+ 3+  0 7+ 11+  0  3 -3
Curve Equation t Generators 51744a1 [0,-1,0,-36438033,-315025068735] 1 [3349129801665284626579551343724021951380547195818589873113:448148986951632688051810549032158459187390461130509583914012:163831221958453345970876297427229799764915871592543671]
51744b (1 curve)	1	2+ 3+ 7+ 11+	2+ 3+  0 7+ 11+  0 -5  5
Curve Equation t Generators 51744b1 [0,-1,0,2287,4929] 1 [79:820:1]
51744c (1 curve)	1	2+ 3+ 7+ 11+	2+ 3+  1 7+ 11+ -2 -3  6
Curve Equation t Generators 51744c1 [0,-1,0,-14520,1395108] 1 [-16:1274:1]
51744d (1 curve)	1	2+ 3+ 7+ 11+	2+ 3+ -2 7+ 11+ -5  4  1
Curve Equation t Generators 51744d1 [0,-1,0,1164371,787158373] 1 [-2742:149171:8]
51744e (2 curves)	0	2+ 3+ 7- 11+	2+ 3+  0 7- 11+  0  0 -8
Curve Equation t 51744e1 [0,-1,0,-9718,-957872] 2 51744e2 [0,-1,0,-217233,-38850111] 2
51744f (1 curve)	0	2+ 3+ 7- 11+	2+ 3+  2 7- 11+  2  1 -1
Curve Equation t 51744f1 [0,-1,0,534623,-156167087] 1
51744g (4 curves)	0	2+ 3+ 7- 11+	2+ 3+  2 7- 11+  2 -2 -4
Curve Equation t 51744g1 [0,-1,0,-7562,253800] 4 51744g2 [0,-1,0,-2417,588225] 2 51744g3 [0,-1,0,-12952,-149372] 2 51744g4 [0,-1,0,-120752,16190952] 2
51744h (1 curve)	0	2+ 3+ 7- 11+	2+ 3+  2 7- 11+  5  4  5
Curve Equation t 51744h1 [0,-1,0,-27197,-1717323] 1
51744i (1 curve)	2	2+ 3+ 7- 11+	2+ 3+  2 7- 11+ -6 -3 -5
Curve Equation t Generators 51744i1 [0,-1,0,-737,7953] 1 [-29:64:1]&[13:20:1]
51744j (2 curves)	0	2+ 3+ 7- 11+	2+ 3+ -2 7- 11+  0  6  2
Curve Equation t 51744j1 [0,-1,0,6746,112288] 2 51744j2 [0,-1,0,-30984,987624] 2
51744k (4 curves)	0	2+ 3+ 7- 11+	2+ 3+ -2 7- 11+  2 -2 -4
Curve Equation t 51744k1 [0,-1,0,-960514,-361988696] 4 51744k2 [0,-1,0,-901224,-408685500] 2 51744k3 [0,-1,0,-1020049,-314515487] 2 51744k4 [0,-1,0,-15367984,-23183421176] 2
51744l (4 curves)	0	2+ 3+ 7- 11+	2+ 3+ -2 7- 11+  2 -6  0
Curve Equation t 51744l1 [0,-1,0,-29514,352584] 4 51744l2 [0,-1,0,116016,2681064] 2 51744l3 [0,-1,0,-293624,-60815292] 2 51744l4 [0,-1,0,-353649,80932545] 2
51744m (2 curves)	0	2+ 3+ 7- 11+	2+ 3+  4 7- 11+ -4 -2 -4
Curve Equation t 51744m1 [0,-1,0,-506,4488] 2 51744m2 [0,-1,0,-16,12328] 2
51744n (2 curves)	2	2+ 3+ 7- 11+	2+ 3+ -4 7- 11+ -6  0 -2
Curve Equation t Generators 51744n1 [0,-1,0,670,-9624] 2 [14:48:1]&[19:98:1] 51744n2 [0,-1,0,-4720,-95864] 2 [-51:98:1]&[121:1044:1]
51744o (2 curves)	1	2+ 3+ 7- 11-	2+ 3+  0 7- 11-  0  0 -8
Curve Equation t Generators 51744o1 [0,-1,0,-198,-2736] 2 [30:132:1] 51744o2 [0,-1,0,-4433,-111999] 2 [107:792:1]
51744p (1 curve)	1	2+ 3+ 7- 11-	2+ 3+  0 7- 11-  0 -3 -3
Curve Equation t Generators 51744p1 [0,-1,0,-743633,-918227967] 1 [4144:259127:1]
51744q (1 curve)	1	2+ 3+ 7- 11-	2+ 3+  0 7- 11-  0  5  5
Curve Equation t Generators 51744q1 [0,-1,0,47,1] 1 [0:1:1]
51744r (2 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11-  0 -6  2
Curve Equation t Generators 51744r1 [0,-1,0,138,288] 2 [6:36:1] 51744r2 [0,-1,0,-632,3060] 2 [-23:70:1]
51744s (1 curve)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11-  1  4  1
Curve Equation t Generators 51744s1 [0,-1,0,6403,963957] 1 [-77:92:1]
51744t (2 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11-  2  0  2
Curve Equation t Generators 51744t1 [0,-1,0,278,-11780] 2 [1020:6110:27] 51744t2 [0,-1,0,-6337,-182447] 2 [161:1716:1]
51744u (4 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11-  2  2  4
Curve Equation t Generators 51744u1 [0,-1,0,-2662,44080] 4 [-56:120:1] 51744u2 [0,-1,0,5423,252673] 2 [-4305:19312:125] 51744u3 [0,-1,0,-12952,-523928] 2 [-4956:5965:64] 51744u4 [0,-1,0,-40392,3137940] 2 [89:490:1]
51744v (4 curves)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11- -2 -2  4
Curve Equation t Generators 51744v1 [0,-1,0,-158482,-24222680] 4 [28901775:1211103256:15625] 51744v2 [0,-1,0,-134472,-31838652] 2 [7328:626450:1] 51744v3 [0,-1,0,-182737,-16291295] 2 [-21884:158025:64] 51744v4 [0,-1,0,-2535472,-1553102648] 2 [759870038204025:20257358743111496:346688140625]
51744w (1 curve)	1	2+ 3+ 7- 11-	2+ 3+  2 7- 11-  5 -4  1
Curve Equation t Generators 51744w1 [0,-1,0,23763,2288133] 1 [371:7876:1]
51744x (4 curves)	1	2+ 3+ 7- 11-	2+ 3+ -2 7- 11- -2  2 -8
Curve Equation t Generators 51744x1 [0,-1,0,-4034,-35496] 4 [166:1960:1] 51744x2 [0,-1,0,14831,-288287] 2 [9316:142155:64] 51744x3 [0,-1,0,-34904,2495844] 4 [89:294:1] 51744x4 [0,-1,0,-52544,-4614840] 2 [265:20:1]
51744y (1 curve)	2	2+ 3- 7+ 11+	2+ 3- -2 7+ 11+ -2 -1  1
Curve Equation t Generators 51744y1 [0,1,0,10911,458415] 1 [-33:252:1]&[39:-972:1]
51744z (1 curve)	2	2+ 3- 7+ 11+	2+ 3- -2 7+ 11+ -5 -4 -5
Curve Equation t Generators 51744z1 [0,1,0,-1332669,591707115] 1 [-915:32340:1]&[702:1617:1]
51744ba (1 curve)	0	2+ 3- 7+ 11+	2+ 3- -2 7+ 11+  6  3  5
Curve Equation t 51744ba1 [0,1,0,-36129,-2655633] 1
51744bb (1 curve)	1	2+ 3- 7+ 11-	2+ 3-  0 7+ 11-  0  3  3
Curve Equation t Generators 51744bb1 [0,1,0,-36438033,315025068735] 1 [3642:480249:1]
51744bc (1 curve)	1	2+ 3- 7+ 11-	2+ 3-  0 7+ 11-  0 -5 -5
Curve Equation t Generators 51744bc1 [0,1,0,2287,-4929] 1 [114:1323:1]
51744bd (1 curve)	1	2+ 3- 7+ 11-	2+ 3- -2 7+ 11- -1 -4 -1
Curve Equation t Generators 51744bd1 [0,1,0,131,-2773] 1 [13:36:1]
51744be (1 curve)	1	2+ 3- 7+ 11-	2+ 3- -2 7+ 11- -5  4 -1
Curve Equation t Generators 51744be1 [0,1,0,1164371,-787158373] 1 [653:15876:1]
51744bf (2 curves)	1	2+ 3- 7- 11+	2+ 3-  0 7- 11+  0  0  8
Curve Equation t Generators 51744bf1 [0,1,0,-198,2736] 2 [9:42:1] 51744bf2 [0,1,0,-4433,111999] 2 [25:132:1]
51744bg (1 curve)	1	2+ 3- 7- 11+	2+ 3-  0 7- 11+  0 -3  3
Curve Equation t Generators 51744bg1 [0,1,0,-743633,918227967] 1 [601:26244:1]
51744bh (1 curve)	1	2+ 3- 7- 11+	2+ 3-  0 7- 11+  0  5 -5
Curve Equation t Generators 51744bh1 [0,1,0,47,-1] 1 [25:132:1]
51744bi (2 curves)	1	2+ 3- 7- 11+	2+ 3-  0 7- 11+  2 -4 -6
Curve Equation t Generators 51744bi1 [0,1,0,-1176898,10642995824] 2 [-355:104958:1] 51744bi2 [0,1,0,-80091888,273303648540] 2 [1626:4055877:8]
51744bj (2 curves)	1	2+ 3- 7- 11+	2+ 3-  0 7- 11+ -4  2  0
Curve Equation t Generators 51744bj1 [0,1,0,-4818,-130320] 2 [81:132:1] 51744bj2 [0,1,0,-4328,-157368] 2 [178:2178:1]
51744bk (1 curve)	1	2+ 3- 7- 11+	2+ 3- -1 7- 11+  2  3 -6
Curve Equation t Generators 51744bk1 [0,1,0,-296,-4152] 1 [34:-162:1]
51744bl (2 curves)	1	2+ 3- 7- 11+	2+ 3-  2 7- 11+  0 -6 -2
Curve Equation t Generators 51744bl1 [0,1,0,138,-288] 2 [9:42:1] 51744bl2 [0,1,0,-632,-3060] 2 [31:90:1]
51744bm (2 curves)	1	2+ 3- 7- 11+	2+ 3-  2 7- 11+  2  0 -2
Curve Equation t Generators 51744bm1 [0,1,0,278,11780] 2 [-10:90:1] 51744bm2 [0,1,0,-6337,182447] 2 [-61:588:1]
51744bn (4 curves)	1	2+ 3- 7- 11+	2+ 3-  2 7- 11+  2  2 -4
Curve Equation t Generators 51744bn1 [0,1,0,-2662,-44080] 4 [51987:2280950:27] 51744bn2 [0,1,0,5423,-252673] 2 [99017569:-535943400:2352637] 51744bn3 [0,1,0,-12952,523928] 2 [7702:675906:1] 51744bn4 [0,1,0,-40392,-3137940] 2 [17868963:780672950:9261]
51744bo (1 curve)	1	2+ 3- 7- 11+	2+ 3-  2 7- 11+  5 -4 -1
Curve Equation t Generators 51744bo1 [0,1,0,23763,-2288133] 1 [174:2673:1]
51744bp (2 curves)	0	2+ 3- 7- 11-	2+ 3-  0 7- 11-  0  0  8
Curve Equation t 51744bp1 [0,1,0,-9718,957872] 2 51744bp2 [0,1,0,-217233,38850111] 2
51744bq (4 curves)	0	2+ 3- 7- 11-	2+ 3-  2 7- 11-  6 -2 -4
Curve Equation t 51744bq1 [0,1,0,-1682,22560] 4 51744bq2 [0,1,0,2728,124872] 2 51744bq3 [0,1,0,-7072,-208132] 2 51744bq4 [0,1,0,-25937,1599135] 2
51744br (2 curves)	0	2+ 3- 7- 11-	2+ 3- -2 7- 11-  0  6 -2
Curve Equation t 51744br1 [0,1,0,6746,-112288] 2 51744br2 [0,1,0,-30984,-987624] 2
51744bs (1 curve)	2	2- 3+ 7+ 11+	2- 3+ -2 7+ 11+ -1 -4  1
Curve Equation t Generators 51744bs1 [0,-1,0,131,2773] 1 [-9:28:1]&[12:77:1]
51744bt (1 curve)	0	2- 3+ 7+ 11+	2- 3+ -4 7+ 11+ -4 -7  7
Curve Equation t 51744bt1 [0,-1,0,-11825,-498399] 1
51744bu (1 curve)	1	2- 3+ 7+ 11-	2- 3+  2 7+ 11- -1  8  1
Curve Equation t Generators 51744bu1 [0,-1,0,-1612557,913217733] 1 [-169:34364:1]
51744bv (1 curve)	1	2- 3+ 7+ 11-	2- 3+ -2 7+ 11- -2 -1 -1
Curve Equation t Generators 51744bv1 [0,-1,0,10911,-458415] 1 [947:29296:1]
51744bw (1 curve)	1	2- 3+ 7+ 11-	2- 3+ -2 7+ 11- -5 -4  5
Curve Equation t Generators 51744bw1 [0,-1,0,-1332669,-591707115] 1 [4660117:258261116:1331]
51744bx (1 curve)	1	2- 3+ 7+ 11-	2- 3+ -2 7+ 11-  6  3 -5
Curve Equation t Generators 51744bx1 [0,-1,0,-36129,2655633] 1 [131:392:1]
51744by (4 curves)	1	2- 3+ 7- 11+	2- 3+  2 7- 11+  6 -2  4
Curve Equation t Generators 51744by1 [0,-1,0,-1682,-22560] 4 [322:5720:1] 51744by2 [0,-1,0,2728,-124872] 2 [429620:3333421:8000] 51744by3 [0,-1,0,-7072,208132] 2 [33:98:1] 51744by4 [0,-1,0,-25937,-1599135] 2 [257:2940:1]
51744bz (1 curve)	1	2- 3+ 7- 11+	2- 3+ -2 7- 11+  1 -8  1
Curve Equation t Generators 51744bz1 [0,-1,0,-32909,2671845] 1 [28:1331:1]
51744ca (2 curves)	0	2- 3+ 7- 11-	2- 3+  0 7- 11-  2 -4  6
Curve Equation t 51744ca1 [0,-1,0,-1176898,-10642995824] 2 51744ca2 [0,-1,0,-80091888,-273303648540] 2
51744cb (2 curves)	0	2- 3+ 7- 11-	2- 3+  0 7- 11- -4  2  0
Curve Equation t 51744cb1 [0,-1,0,-4818,130320] 2 51744cb2 [0,-1,0,-4328,157368] 2
51744cc (1 curve)	0	2- 3+ 7- 11-	2- 3+ -1 7- 11-  2  3  6
Curve Equation t 51744cc1 [0,-1,0,-296,4152] 1
51744cd (1 curve)	0	2- 3+ 7- 11-	2- 3+  4 7- 11-  4  7  7
Curve Equation t 51744cd1 [0,-1,0,-579441,-172109727] 1
51744ce (1 curve)	1	2- 3- 7+ 11+	2- 3-  2 7+ 11+ -1  8 -1
Curve Equation t Generators 51744ce1 [0,1,0,-1612557,-913217733] 1 [17082:586971:8]
51744cf (1 curve)	0	2- 3- 7+ 11-	2- 3-  1 7+ 11- -2 -3 -6
Curve Equation t 51744cf1 [0,1,0,-14520,-1395108] 1
51744cg (1 curve)	2	2- 3- 7+ 11-	2- 3- -4 7+ 11- -4 -7 -7
Curve Equation t Generators 51744cg1 [0,1,0,-11825,498399] 1 [79:-252:1]&[-110:693:1]
51744ch (1 curve)	0	2- 3- 7- 11+	2- 3-  2 7- 11+  1  4 -1
Curve Equation t 51744ch1 [0,1,0,6403,-963957] 1
51744ci (4 curves)	0	2- 3- 7- 11+	2- 3-  2 7- 11+ -2 -2 -4
Curve Equation t 51744ci1 [0,1,0,-158482,24222680] 4 51744ci2 [0,1,0,-134472,31838652] 2 51744ci3 [0,1,0,-182737,16291295] 2 51744ci4 [0,1,0,-2535472,1553102648] 2
51744cj (4 curves)	0	2- 3- 7- 11+	2- 3- -2 7- 11+ -2  2  8
Curve Equation t 51744cj1 [0,1,0,-4034,35496] 4 51744cj2 [0,1,0,14831,288287] 4 51744cj3 [0,1,0,-34904,-2495844] 2 51744cj4 [0,1,0,-52544,4614840] 2
51744ck (1 curve)	0	2- 3- 7- 11+	2- 3-  4 7- 11+  4  7 -7
Curve Equation t 51744ck1 [0,1,0,-579441,172109727] 1
51744cl (1 curve)	1	2- 3- 7- 11-	2- 3-  2 7- 11-  2  1  1
Curve Equation t Generators 51744cl1 [0,1,0,534623,156167087] 1 [-211:5832:1]
51744cm (4 curves)	1	2- 3- 7- 11-	2- 3-  2 7- 11-  2 -2  4
Curve Equation t Generators 51744cm1 [0,1,0,-7562,-253800] 4 [-4425300:-3344985:85184] 51744cm2 [0,1,0,-2417,-588225] 2 [1875:81180:1] 51744cm3 [0,1,0,-12952,149372] 2 [-838:4851:8] 51744cm4 [0,1,0,-120752,-16190952] 2 [-147459021687780:-562614614541:733870808000]
51744cn (1 curve)	1	2- 3- 7- 11-	2- 3-  2 7- 11-  5  4 -5
Curve Equation t Generators 51744cn1 [0,1,0,-27197,1717323] 1 [97:36:1]
51744co (1 curve)	1	2- 3- 7- 11-	2- 3-  2 7- 11- -6 -3  5
Curve Equation t Generators 51744co1 [0,1,0,-737,-7953] 1 [302271:1488528:6859]
51744cp (1 curve)	1	2- 3- 7- 11-	2- 3- -2 7- 11-  1 -8 -1
Curve Equation t Generators 51744cp1 [0,1,0,-32909,-2671845] 1 [577:13068:1]
51744cq (4 curves)	1	2- 3- 7- 11-	2- 3- -2 7- 11-  2 -2  4
Curve Equation t Generators 51744cq1 [0,1,0,-960514,361988696] 4 [650:-3564:1] 51744cq2 [0,1,0,-901224,408685500] 2 [639:9702:1] 51744cq3 [0,1,0,-1020049,314515487] 2 [-61:19404:1] 51744cq4 [0,1,0,-15367984,23183421176] 2 [2267:330:1]
51744cr (4 curves)	1	2- 3- 7- 11-	2- 3- -2 7- 11-  2 -6  0
Curve Equation t Generators 51744cr1 [0,1,0,-29514,-352584] 4 [-159:588:1] 51744cr2 [0,1,0,116016,-2681064] 2 [39:1380:1] 51744cr3 [0,1,0,-293624,60815292] 2 [79:6174:1] 51744cr4 [0,1,0,-353649,-80932545] 2 [-333:132:1]
51744cs (2 curves)	1	2- 3- 7- 11-	2- 3-  4 7- 11- -4 -2  4
Curve Equation t Generators 51744cs1 [0,1,0,-506,-4488] 2 [115545:3513798:125] 51744cs2 [0,1,0,-16,-12328] 2 [3698:224910:1]
51744ct (2 curves)	1	2- 3- 7- 11-	2- 3- -4 7- 11- -6  0  2
Curve Equation t Generators 51744ct1 [0,1,0,670,9624] 2 [10:132:1] 51744ct2 [0,1,0,-4720,95864] 2 [2:294:1]

Data from Elliptic Curve Data by J. E. Cremona.
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Part of Computational Number Theory
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