Cremona's table of elliptic curves

68208 = 2⁴ · 3 · 7² · 29

Class	r	Atkin-Lehner	Eigenvalues
68208a (1 curve)	1	2+ 3+ 7+ 29+	2+ 3+ -1 7+  6 -5  0  4
Curve Equation t Generators 68208a1 [0,-1,0,-17688281,-19329418443] 1 [541532:398494803:1]
68208b (1 curve)	2	2+ 3+ 7+ 29-	2+ 3+ -1 7+  0 -5  0 -2
Curve Equation t Generators 68208b1 [0,-1,0,-85521,9615789] 1 [1146:-4263:8]&[20:2813:1]
68208c (1 curve)	0	2+ 3+ 7- 29+	2+ 3+  0 7-  3 -1  1  0
Curve Equation t 68208c1 [0,-1,0,-4328,111063] 1
68208d (2 curves)	2	2+ 3+ 7- 29+	2+ 3+  0 7- -4  0  0  0
Curve Equation t Generators 68208d1 [0,-1,0,5472,327888] 2 [54:-882:1]&[-36:288:1] 68208d2 [0,-1,0,-51368,3874704] 2 [-254:686:1]&[40:1372:1]
68208e (2 curves)	0	2+ 3+ 7- 29+	2+ 3+  0 7- -4  6 -6  0
Curve Equation t 68208e1 [0,-1,0,-53689708,-152498924864] 2 68208e2 [0,-1,0,-860761848,-9719854901280] 2
68208f (1 curve)	0	2+ 3+ 7- 29+	2+ 3+ -1 7-  2 -4 -5  5
Curve Equation t 68208f1 [0,-1,0,-290096,60263904] 1
68208g (2 curves)	0	2+ 3+ 7- 29+	2+ 3+ -2 7-  0 -2  2  0
Curve Equation t 68208g1 [0,-1,0,-17264,-2692080] 2 68208g2 [0,-1,0,-415144,-102639536] 2
68208h (1 curve)	2	2+ 3+ 7- 29+	2+ 3+ -3 7-  2 -3  0  0
Curve Equation t Generators 68208h1 [0,-1,0,-457,-3611] 1 [-12:1:1]&[28:69:1]
68208i (2 curves)	0	2+ 3+ 7- 29+	2+ 3+  4 7-  4 -2  2  8
Curve Equation t 68208i1 [0,-1,0,964,-13152] 2 68208i2 [0,-1,0,-5896,-122912] 2
68208j (1 curve)	0	2+ 3+ 7- 29+	2+ 3+ -4 7- -1 -1  1 -4
Curve Equation t 68208j1 [0,-1,0,-1780,-33389] 1
68208k (1 curve)	1	2+ 3+ 7- 29-	2+ 3+  0 7-  3  5  2 -3
Curve Equation t Generators 68208k1 [0,-1,0,-2088,37584] 1 [26:-14:1]
68208l (4 curves)	1	2+ 3+ 7- 29-	2+ 3+  2 7-  0 -6 -6 -4
Curve Equation t Generators 68208l1 [0,-1,0,1993,-68718] 2 [137572482:1842329440:804357] 68208l2 [0,-1,0,-17852,-775200] 4 [18804:486080:27] 68208l3 [0,-1,0,-79592,7917792] 4 [-247:3528:1] 68208l4 [0,-1,0,-273632,-55000560] 2 [2784:144060:1]
68208m (1 curve)	1	2+ 3+ 7- 29-	2+ 3+  2 7-  5 -1  7  2
Curve Equation t Generators 68208m1 [0,-1,0,2728,-479877] 1 [525623:4974283:4913]
68208n (1 curve)	1	2+ 3+ 7- 29-	2+ 3+ -3 7-  4 -3  8 -2
Curve Equation t Generators 68208n1 [0,-1,0,-4097,-77139] 1 [1364:50301:1]
68208o (1 curve)	0	2+ 3- 7+ 29+	2+ 3-  3 7+  2  3  0  0
Curve Equation t 68208o1 [0,1,0,-22409,1283379] 1
68208p (1 curve)	1	2+ 3- 7+ 29-	2+ 3-  3 7+  4  3 -8  2
Curve Equation t Generators 68208p1 [0,1,0,-200769,26860203] 1 [-474:3969:1]
68208q (1 curve)	1	2+ 3- 7- 29+	2+ 3-  1 7-  6  5  0 -4
Curve Equation t Generators 68208q1 [0,1,0,-360985,56250851] 1 [-154187960766:2524913213761:275894451]
68208r (2 curves)	1	2+ 3- 7- 29+	2+ 3-  2 7-  0  2 -2  0
Curve Equation t Generators 68208r1 [0,1,0,-352,7748] 2 [2:-84:1] 68208r2 [0,1,0,-8472,296820] 2 [-12:630:1]
68208s (1 curve)	1	2+ 3- 7- 29+	2+ 3-  2 7-  3  7 -3 -6
Curve Equation t Generators 68208s1 [0,1,0,-212,2127] 1 [-11:57:1]
68208t (4 curves)	1	2+ 3- 7- 29+	2+ 3-  2 7- -4  2  2 -4
Curve Equation t Generators 68208t1 [0,1,0,9588,-19188] 2 [27:510:1] 68208t2 [0,1,0,-38432,-192060] 4 [-152:1470:1] 68208t3 [0,1,0,-408872,100123092] 2 [394:588:1] 68208t4 [0,1,0,-436312,-110802700] 2 [1628:59130:1]
68208u (4 curves)	1	2+ 3- 7- 29+	2+ 3-  2 7- -4  6  6 -4
Curve Equation t Generators 68208u1 [0,1,0,-10012,382220] 2 [20255:217974:125] 68208u2 [0,1,0,-10992,301860] 4 [608:14790:1] 68208u3 [0,1,0,30168,2063508] 2 [6540:4916366:3375] 68208u4 [0,1,0,-67832,-6587148] 2 [394:5292:1]
68208v (1 curve)	1	2+ 3- 7- 29+	2+ 3- -2 7-  3  5 -6  5
Curve Equation t Generators 68208v1 [0,1,0,-1022744,462307572] 1 [268:-14406:1]
68208w (1 curve)	1	2+ 3- 7- 29+	2+ 3-  3 7-  2 -4 -7  7
Curve Equation t Generators 68208w1 [0,1,0,376,-6252] 1 [186:2556:1]
68208x (1 curve)	0	2+ 3- 7- 29-	2+ 3-  0 7-  3 -5 -2  3
Curve Equation t 68208x1 [0,1,0,-102328,-12686668] 1
68208y (1 curve)	0	2+ 3- 7- 29-	2+ 3-  0 7-  5 -1  3 -4
Curve Equation t 68208y1 [0,1,0,572,1931] 1
68208z (1 curve)	0	2+ 3- 7- 29-	2+ 3-  1 7-  0  5  0  2
Curve Equation t 68208z1 [0,1,0,-1745,-28533] 1
68208ba (2 curves)	0	2- 3+ 7+ 29+	2- 3+  0 7+  0  5  6  7
Curve Equation t 68208ba1 [0,-1,0,-86893,-12370511] 1 68208ba2 [0,-1,0,653987,115653553] 1
68208bb (1 curve)	1	2- 3+ 7+ 29-	2- 3+  3 7+  0  3  4 -6
Curve Equation t Generators 68208bb1 [0,-1,0,-1829,-3303] 1 [-16:147:1]
68208bc (1 curve)	1	2- 3+ 7- 29+	2- 3+  0 7- -1 -5 -6  1
Curve Equation t Generators 68208bc1 [0,-1,0,152,-272] 1 [12:-56:1]
68208bd (2 curves)	1	2- 3+ 7- 29+	2- 3+  0 7- -2  0 -2 -4
Curve Equation t Generators 68208bd1 [0,-1,0,2287,40944] 2 [61000:722331:512] 68208bd2 [0,-1,0,-13148,399036] 2 [497:10788:1]
68208be (2 curves)	1	2- 3+ 7- 29+	2- 3+  0 7-  4  0  4 -4
Curve Equation t Generators 68208be1 [0,-1,0,-393838888,-3008441170832] 2 [753709793681615003425265959012:141382683289487401163405614209024:16624105182023530648068793] 68208be2 [0,-1,0,-6301561128,-192537622985616] 2 [40242349024426619934011228419438033976144837497809870:-4713408460409993975990828654895415875166393612907238918:410496860223955035290093461569353873347799537951]
68208bf (2 curves)	1	2- 3+ 7- 29+	2- 3+  0 7- -4  4  0  4
Curve Equation t Generators 68208bf1 [0,-1,0,-20568,5212656] 2 [-198:1218:1] 68208bf2 [0,-1,0,-594008,175868400] 2 [418:658:1]
68208bg (1 curve)	1	2- 3+ 7- 29+	2- 3+  1 7-  2  5  4 -4
Curve Equation t Generators 68208bg1 [0,-1,0,-300925,63610849] 1 [280:1107:1]
68208bh (1 curve)	1	2- 3+ 7- 29+	2- 3+  1 7- -2 -7 -4 -4
Curve Equation t Generators 68208bh1 [0,-1,0,-485,2829] 1 [20:27:1]
68208bi (1 curve)	1	2- 3+ 7- 29+	2- 3+ -1 7- -6  4  7 -3
Curve Equation t Generators 68208bi1 [0,-1,0,-3936,-102528] 1 [104:776:1]
68208bj (2 curves)	1	2- 3+ 7- 29+	2- 3+  2 7-  0  0  4  4
Curve Equation t Generators 68208bj1 [0,-1,0,-352,-1280] 2 [-15:20:1] 68208bj2 [0,-1,0,-2592,50688] 2 [-54:174:1]
68208bk (1 curve)	1	2- 3+ 7- 29+	2- 3+  2 7- -3  1 -2  3
Curve Equation t Generators 68208bk1 [0,-1,0,131900928,-1058272247808] 1 [2755410118056928498:253825337538912594742:336877494249941]
68208bl (1 curve)	1	2- 3+ 7- 29+	2- 3+  2 7- -3 -5  1  6
Curve Equation t Generators 68208bl1 [0,-1,0,-4622,1353507] 1 [-20878153:179339623:205379]
68208bm (1 curve)	1	2- 3+ 7- 29+	2- 3+ -2 7- -1 -1 -2 -1
Curve Equation t Generators 68208bm1 [0,-1,0,-7464,-504720] 1 [292:4704:1]
68208bn (2 curves)	1	2- 3+ 7- 29+	2- 3+ -4 7-  0 -2 -2  0
Curve Equation t Generators 68208bn1 [0,-1,0,-345760,88251136] 2 [-240:12544:1] 68208bn2 [0,-1,0,-5724000,5272874496] 2 [1370:686:1]
68208bo (2 curves)	0	2- 3+ 7- 29-	2- 3+  0 7-  0  6  2  0
Curve Equation t 68208bo1 [0,-1,0,-408,69168] 2 68208bo2 [0,-1,0,-27848,1781424] 2
68208bp (2 curves)	0	2- 3+ 7- 29-	2- 3+  0 7- -2 -2  4 -4
Curve Equation t 68208bp1 [0,-1,0,96367,166750116] 2 68208bp2 [0,-1,0,-4021348,3006326380] 2
68208bq (1 curve)	0	2- 3+ 7- 29-	2- 3+  0 7-  3  3 -1 -4
Curve Equation t 68208bq1 [0,-1,0,82,519] 1
68208br (2 curves)	0	2- 3+ 7- 29-	2- 3+  0 7-  4  4  4  8
Curve Equation t 68208br1 [0,-1,0,-159168,-74105856] 2 68208br2 [0,-1,0,-3796928,-2841713664] 2
68208bs (2 curves)	0	2- 3+ 7- 29-	2- 3+  2 7-  0 -4  0 -4
Curve Equation t 68208bs1 [0,-1,0,-91352,10643760] 2 68208bs2 [0,-1,0,-118792,3750832] 2
68208bt (2 curves)	0	2- 3+ 7- 29-	2- 3+  2 7-  0 -6 -6  8
Curve Equation t 68208bt1 [0,-1,0,-105072,-13508928] 2 68208bt2 [0,-1,0,-1696592,-850011840] 2
68208bu (1 curve)	0	2- 3+ 7- 29-	2- 3+  2 7- -1  5 -2 -5
Curve Equation t 68208bu1 [0,-1,0,861208,3497352048] 1
68208bv (2 curves)	0	2- 3+ 7- 29-	2- 3+  2 7-  2  2 -8  4
Curve Equation t 68208bv1 [0,-1,0,-4377,112680] 2 68208bv2 [0,-1,0,-6092,18012] 2
68208bw (6 curves)	0	2- 3+ 7- 29-	2- 3+  2 7- -4  2 -2 -4
Curve Equation t 68208bw1 [0,-1,0,-614672,198801408] 2 68208bw2 [0,-1,0,-10026592,12223470400] 4 68208bw3 [0,-1,0,-10218672,11730977280] 4 68208bw4 [0,-1,0,-160425232,782144188288] 2 68208bw5 [0,-1,0,9785088,52042554432] 4 68208bw6 [0,-1,0,-33295712,-60103232832] 2
68208bx (2 curves)	0	2- 3+ 7- 29-	2- 3+ -2 7-  0 -2  6  0
Curve Equation t 68208bx1 [0,-1,0,103136,1654528] 2 68208bx2 [0,-1,0,-416544,13711104] 2
68208by (2 curves)	0	2- 3+ 7- 29-	2- 3+ -2 7-  6  4  6  0
Curve Equation t 68208by1 [0,-1,0,-5889,-171996] 2 68208by2 [0,-1,0,-5924,-169812] 2
68208bz (1 curve)	0	2- 3+ 7- 29-	2- 3+ -3 7- -6  0 -7  5
Curve Equation t 68208bz1 [0,-1,0,-44312,-3684624] 1
68208ca (1 curve)	0	2- 3+ 7- 29-	2- 3+ -4 7- -3  3 -6  5
Curve Equation t 68208ca1 [0,-1,0,5360,-1292864] 1
68208cb (1 curve)	0	2- 3+ 7- 29-	2- 3+ -4 7- -4 -1 -2 -1
Curve Equation t 68208cb1 [0,-1,0,-12805,-7814099] 1
68208cc (1 curve)	1	2- 3- 7+ 29+	2- 3- -1 7+  2 -5 -4  4
Curve Equation t Generators 68208cc1 [0,1,0,-6141,-187209] 1 [-45:6:1]
68208cd (1 curve)	1	2- 3- 7+ 29+	2- 3- -1 7+ -2  7  4  4
Curve Equation t Generators 68208cd1 [0,1,0,-23781,-922797] 1 [-66:603:1]
68208ce (1 curve)	0	2- 3- 7+ 29-	2- 3-  4 7+ -4  1  2  1
Curve Equation t 68208ce1 [0,1,0,-261,22707] 1
68208cf (4 curves)	0	2- 3- 7- 29+	2- 3-  0 7-  0 -2  6  8
Curve Equation t 68208cf1 [0,1,0,-104288,18494580] 2 68208cf2 [0,1,0,-1860448,975953012] 2 68208cf3 [0,1,0,836512,-258401676] 2 68208cf4 [0,1,0,-4541728,-2386033420] 2
68208cg (2 curves)	2	2- 3- 7- 29+	2- 3-  0 7-  0 -5 -6 -7
Curve Equation t Generators 68208cg1 [0,1,0,-1773,35559] 1 [-45:162:1]&[3:174:1] 68208cg2 [0,1,0,13347,-333369] 1 [1758:24389:27]&[111:1590:1]
68208ch (1 curve)	0	2- 3- 7- 29+	2- 3-  0 7- -1  5  6 -1
Curve Equation t 68208ch1 [0,1,0,7432,78420] 1
68208ci (2 curves)	0	2- 3- 7- 29+	2- 3-  0 7- -2  0  2  4
Curve Equation t 68208ci1 [0,1,0,47,-106] 2 68208ci2 [0,1,0,-268,-1240] 2
68208cj (2 curves)	0	2- 3- 7- 29+	2- 3-  0 7-  4  0 -4  4
Curve Equation t 68208cj1 [0,1,0,-8037528,8768669076] 2 68208cj2 [0,1,0,-128603288,561297434004] 2
68208ck (2 curves)	0	2- 3- 7- 29+	2- 3-  0 7- -4 -4  0 -4
Curve Equation t 68208ck1 [0,1,0,-1007848,-1785925324] 2 68208ck2 [0,1,0,-29106408,-60264648396] 2
68208cl (2 curves)	0	2- 3- 7- 29+	2- 3- -2 7-  0  0 -4 -4
Curve Equation t 68208cl1 [0,1,0,-17264,473556] 2 68208cl2 [0,1,0,-127024,-17131948] 2
68208cm (4 curves)	0	2- 3- 7- 29+	2- 3- -2 7-  4 -6  2  4
Curve Equation t 68208cm1 [0,1,0,376,-39180] 2 68208cm2 [0,1,0,-15304,-710284] 4 68208cm3 [0,1,0,-38824,1970996] 2 68208cm4 [0,1,0,-242664,-46091340] 2
68208cn (2 curves)	0	2- 3- 7- 29+	2- 3-  3 7- -6  4 -3 -1
Curve Equation t 68208cn1 [0,1,0,-6040344,26936038548] 1 68208cn2 [0,1,0,53970936,-698408300556] 1
68208co (1 curve)	0	2- 3- 7- 29+	2- 3-  4 7-  1  3  5  4
Curve Equation t 68208co1 [0,1,0,-2466,49167] 1
68208cp (2 curves)	1	2- 3- 7- 29-	2- 3-  0 7-  0  6  2  0
Curve Equation t Generators 68208cp1 [0,1,0,85832,2248532] 2 [23:2058:1] 68208cp2 [0,1,0,-353208,17878356] 2 [-516:7938:1]
68208cq (2 curves)	1	2- 3- 7- 29-	2- 3-  1 7-  2  0  3 -1
Curve Equation t Generators 68208cq1 [0,1,0,-800,3009012] 1 [-38:1728:1] 68208cq2 [0,1,0,-5104640,-4453795788] 1 [2706:39432:1]
68208cr (2 curves)	1	2- 3- 7- 29-	2- 3-  2 7-  0  2 -6  0
Curve Equation t Generators 68208cr1 [0,1,0,5053648,-577610412] 2 [172:17226:1] 68208cr2 [0,1,0,-20410672,-4662087340] 2 [87980:26061750:1]
68208cs (2 curves)	1	2- 3- 7- 29-	2- 3-  2 7-  6 -4 -6  0
Curve Equation t Generators 68208cs1 [0,1,0,-288577,59571770] 2 [3941926780:-20240242107:10648000] 68208cs2 [0,1,0,-290292,58826088] 2 [-7445:1089066:125]
68208ct (2 curves)	1	2- 3- 7- 29-	2- 3- -2 7-  0  4  0  4
Curve Equation t Generators 68208ct1 [0,1,0,-1864,-31564] 2 [-25:6:1] 68208ct2 [0,1,0,-2424,-11628] 2 [-36:174:1]
68208cu (2 curves)	1	2- 3- 7- 29-	2- 3- -2 7-  0  6  6 -8
Curve Equation t Generators 68208cu1 [0,1,0,-2144,38772] 2 [4:174:1] 68208cu2 [0,1,0,-34624,2468276] 2 [100:126:1]
68208cv (1 curve)	1	2- 3- 7- 29-	2- 3- -2 7- -1  3  3  2
Curve Equation t Generators 68208cv1 [0,1,0,-114,-813] 1 [146471:1187913:2197]
68208cw (2 curves)	1	2- 3- 7- 29-	2- 3- -2 7-  2 -6  0 -4
Curve Equation t Generators 68208cw1 [0,1,0,-43969,3360146] 2 [254:2940:1] 68208cw2 [0,1,0,-128004,-13413240] 2 [-201:2058:1]
68208cx (4 curves)	1	2- 3- 7- 29-	2- 3- -2 7- -4  6 -6 -4
Curve Equation t Generators 68208cx1 [0,1,0,-3270085184,-97314934676940] 2 [75508:9288642:1] 68208cx2 [0,1,0,-57283545664,-5276492817030604] 4 [69945167607058:33618940375071744:172808693] 68208cx3 [0,1,0,-62274552384,-4302577711730124] 4 [15051939192285384444:-18891000701647039046250:9318005566507] 68208cx4 [0,1,0,-916507906624,-337716928177597900] 2 [1619018:1556356032:1]
68208cy (4 curves)	1	2- 3- 7- 29-	2- 3- -2 7- -4 -6  6 -4
Curve Equation t Generators 68208cy1 [0,1,0,-554304,-152006604] 2 [715552886274:53494961766400:125751501] 68208cy2 [0,1,0,-1557824,552464436] 4 [22084:479457:64] 68208cy3 [0,1,0,3898816,3566712372] 2 [-726:18816:1] 68208cy4 [0,1,0,-23070784,42640419380] 4 [-4828:203742:1]
68208cz (1 curve)	1	2- 3- 7- 29-	2- 3- -2 7-  5 -3 -6  5
Curve Equation t Generators 68208cz1 [0,1,0,-32944,2304980] 1 [-68:2058:1]
68208da (1 curve)	1	2- 3- 7- 29-	2- 3- -3 7-  0 -3 -4  6
Curve Equation t Generators 68208da1 [0,1,0,-37,-1] 1 [-1:6:1]
68208db (1 curve)	1	2- 3- 7- 29-	2- 3-  4 7- -3 -3  6 -5
Curve Equation t Generators 68208db1 [0,1,0,262624,442927092] 1 [-572:10290:1]
68208dc (2 curves)	1	2- 3- 7- 29-	2- 3-  4 7- -4  0  0  8
Curve Equation t Generators 68208dc1 [0,1,0,35264,-2243788] 2 [5916:108170:27] 68208dc2 [0,1,0,-192096,-20887308] 2 [1458:52920:1]

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