Cremona's table of elliptic curves

117117 = 3² · 7 · 11 · 13²

Class	r	Atkin-Lehner	Eigenvalues
117117a (2 curves)	1	3+ 7+ 11+ 13+	0 3+  0 7+ 11+ 13+  0 -2
Curve Equation t Generators 117117a1 [0,0,1,5070,-1330833] 1 [117:929:1] 117117a2 [0,0,1,-775710,-263035276] 1 [126282:8470520:27]
117117b (2 curves)	2	3+ 7+ 11+ 13-	1 3+ -2 7+ 11+ 13- -4  0
Curve Equation t Generators 117117b1 [1,-1,0,-190293,-31925880] 2 [556:5546:1]&[7854:211743:8] 117117b2 [1,-1,0,-3045288,-2044697355] 2 [6796:536141:1]&[92294:9746013:8]
117117c (1 curve)	2	3+ 7+ 11+ 13-	-2 3+ -2 7+ 11+ 13-  2 -6
Curve Equation t Generators 117117c1 [0,0,1,39,42] 1 [-1:1:1]&[0:6:1]
117117d (2 curves)	2	3+ 7+ 11- 13+	0 3+  0 7+ 11- 13+  0 -2
Curve Equation t Generators 117117d1 [0,0,1,-86190,9742047] 1 [-13:3295:1]&[185:358:1] 117117d2 [0,0,1,45630,35932484] 1 [-182:4647:1]&[546:50189:8]
117117e (2 curves)	1	3+ 7+ 11- 13-	-1 3+  2 7+ 11- 13-  4  0
Curve Equation t Generators 117117e1 [1,-1,1,-1712639,863711398] 2 [62:27496:1] 117117e2 [1,-1,1,-27407594,55234236178] 2 [3329:27980:1]
117117f (1 curve)	1	3+ 7+ 11- 13-	2 3+  2 7+ 11- 13- -2 -6
Curve Equation t Generators 117117f1 [0,0,1,351,-1141] 1 [962:10669:8]
117117g (2 curves)	1	3+ 7- 11+ 13-	1 3+ -2 7- 11+ 13-  4  0
Curve Equation t Generators 117117g1 [1,-1,0,-289435938,1896705634175] 2 [335493015495946:-67529518577682073:7335308807] 117117g2 [1,-1,0,-4631883333,121335721233650] 2 [11817425026:-6103219892:300763]
117117h (1 curve)	1	3+ 7- 11+ 13-	-2 3+ -2 7- 11+ 13- -2  6
Curve Equation t Generators 117117h1 [0,0,1,59319,-2506228] 1 [338:2193:8]
117117i (2 curves)	0	3+ 7- 11- 13-	-1 3+  2 7- 11- 13- -4  0
Curve Equation t 117117i1 [1,-1,1,-32159549,-70237636972] 2 117117i2 [1,-1,1,-514653704,-4493744050012] 2
117117j (1 curve)	0	3+ 7- 11- 13-	2 3+  2 7- 11- 13-  2  6
Curve Equation t 117117j1 [0,0,1,6591,92823] 1
117117k (2 curves)	0	3- 7+ 11+ 13+	0 3-  0 7+ 11+ 13+  6  1
Curve Equation t 117117k1 [0,0,1,-390,-2961] 1 117117k2 [0,0,1,-1560,20790] 1
117117l (1 curve)	0	3- 7+ 11+ 13+	0 3- -1 7+ 11+ 13+  4 -7
Curve Equation t 117117l1 [0,0,1,-49860408,-135560187630] 1
117117m (1 curve)	0	3- 7+ 11+ 13+	0 3-  3 7+ 11+ 13+ -4 -7
Curve Equation t 117117m1 [0,0,1,10039614,1158291904] 1
117117n (3 curves)	0	3- 7+ 11+ 13+	0 3-  3 7+ 11+ 13+  6 -2
Curve Equation t 117117n1 [0,0,1,-135876,-19278126] 1 117117n2 [0,0,1,-75036,-36579501] 1 117117n3 [0,0,1,670254,946830654] 1
117117o (2 curves)	0	3- 7+ 11+ 13+	1 3-  0 7+ 11+ 13+  0  8
Curve Equation t 117117o1 [1,-1,0,-5271057,-7041739496] 2 117117o2 [1,-1,0,-95823792,-360939938423] 2
117117p (4 curves)	0	3- 7+ 11+ 13+	1 3- -2 7+ 11+ 13+  6 -4
Curve Equation t 117117p1 [1,-1,0,-139203,-10290344] 2 117117p2 [1,-1,0,-1059408,412819915] 4 117117p3 [1,-1,0,28107,1219103536] 2 117117p4 [1,-1,0,-16870203,26674550410] 2
117117q (1 curve)	0	3- 7+ 11+ 13+	1 3-  4 7+ 11+ 13+  3  8
Curve Equation t 117117q1 [1,-1,0,-5355,-4233722] 1
117117r (6 curves)	2	3- 7+ 11+ 13+	-1 3- -2 7+ 11+ 13+ -2 -4
Curve Equation t Generators 117117r1 [1,-1,1,-51746,-4516248] 2 [-132:99:1]&[-130:96:1] 117117r2 [1,-1,1,-59351,-3095634] 4 [-202:888:1]&[-198:1028:1] 117117r3 [1,-1,1,191614,-22570518] 2 [153:3134:1]&[13054:537987:8] 117117r4 [1,-1,1,-431996,107207286] 4 [-718:7203:1]&[-4418:108675:8] 117117r5 [1,-1,1,47119,331624752] 2 [-627:7749:1]&[-3554:121203:8] 117117r6 [1,-1,1,-6873431,6937704960] 2 [794:44103:1]&[1388:7671:1]
117117s (1 curve)	2	3- 7+ 11+ 13+	-1 3- -3 7+ 11+ 13+  3  0
Curve Equation t Generators 117117s1 [1,-1,1,436,-1816] 1 [6:28:1]&[13:-84:1]
117117t (1 curve)	0	3- 7+ 11+ 13+	2 3-  0 7+ 11+ 13+  2 -7
Curve Equation t 117117t1 [0,0,1,-7605,254387] 1
117117u (1 curve)	2	3- 7+ 11+ 13+	2 3-  0 7+ 11+ 13+ -6 -6
Curve Equation t Generators 117117u1 [0,0,1,-149565,22660407] 1 [-2990:41063:8]&[2002:7601:8]
117117v (1 curve)	0	3- 7+ 11+ 13+	-2 3-  0 7+ 11+ 13+  6  2
Curve Equation t 117117v1 [0,0,1,2862015,1962182992] 1
117117w (1 curve)	0	3- 7+ 11+ 13+	-2 3- -2 7+ 11+ 13+ -6 -1
Curve Equation t 117117w1 [0,0,1,-3080181,1720997320] 1
117117x (1 curve)	0	3- 7+ 11+ 13+	-2 3- -4 7+ 11+ 13+  2  5
Curve Equation t 117117x1 [0,0,1,-573417,-124347454] 1
117117y (2 curves)	1	3- 7+ 11+ 13-	1 3- -2 7+ 11+ 13-  2  0
Curve Equation t Generators 117117y1 [1,-1,0,-25128,-979965] 2 [2574378:151524179:729] 117117y2 [1,-1,0,73737,-6852546] 2 [14118:1670694:1]
117117z (2 curves)	1	3- 7+ 11+ 13-	-1 3-  0 7+ 11+ 13- -2 -4
Curve Equation t Generators 117117z1 [1,-1,1,-4588557395,119635801234850] 2 [10875129180:-2024912449025:438976] 117117z2 [1,-1,1,-4456968080,126819946205138] 2 [1674826273549034739228:-327880886237709664860497:62906131876318912]
117117ba (1 curve)	1	3- 7+ 11- 13+	0 3- -1 7+ 11- 13+  4  1
Curve Equation t Generators 117117ba1 [0,0,1,-2028,899122] 1 [26:-930:1]
117117bb (1 curve)	1	3- 7+ 11- 13+	0 3-  2 7+ 11- 13+ -2  7
Curve Equation t Generators 117117bb1 [0,0,1,-52200174,145163033239] 1 [277641709:1095648906:68921]
117117bc (2 curves)	0	3- 7+ 11- 13-	1 3-  2 7+ 11- 13-  0  4
Curve Equation t 117117bc1 [1,-1,0,-2219931,1353024544] 2 117117bc2 [1,-1,0,-36130626,83600024197] 2
117117bd (2 curves)	0	3- 7+ 11- 13-	1 3-  2 7+ 11- 13-  0  4
Curve Equation t 117117bd1 [1,-1,0,272169,51923704] 2 117117bd2 [1,-1,0,-1533726,487866757] 2
117117be (2 curves)	0	3- 7+ 11- 13-	1 3- -4 7+ 11- 13- -6  4
Curve Equation t 117117be1 [1,-1,0,-2079,-28976] 2 117117be2 [1,-1,0,4356,-176981] 2
117117bf (2 curves)	2	3- 7+ 11- 13-	-1 3-  0 7+ 11- 13- -2 -4
Curve Equation t Generators 117117bf1 [1,-1,1,2425,7310] 2 [6:-152:1]&[30:1007:8] 117117bf2 [1,-1,1,-9860,66278] 2 [-84:586:1]&[6:82:1]
117117bg (1 curve)	0	3- 7+ 11- 13-	-2 3- -1 7+ 11- 13-  6  7
Curve Equation t 117117bg1 [0,0,1,-481143,-908461148] 1
117117bh (1 curve)	1	3- 7- 11+ 13+	0 3- -1 7- 11+ 13+ -2  1
Curve Equation t Generators 117117bh1 [0,0,1,-24155508,-45861269360] 1 [61750:15294415:1]
117117bi (1 curve)	1	3- 7- 11+ 13+	0 3- -1 7- 11+ 13+ -2  6
Curve Equation t Generators 117117bi1 [0,0,1,3042,-14830] 1 [130:1605:1]
117117bj (1 curve)	1	3- 7- 11+ 13+	0 3- -2 7- 11+ 13+ -2 -7
Curve Equation t Generators 117117bj1 [0,0,1,-8821829406,318923184026632] 1 [54206:8403:1]
117117bk (2 curves)	0	3- 7- 11+ 13-	1 3-  0 7- 11+ 13- -2  4
Curve Equation t 117117bk1 [1,-1,0,409878,17290287] 2 117117bk2 [1,-1,0,-1666287,140614488] 2
117117bl (2 curves)	2	3- 7- 11+ 13-	-1 3- -2 7- 11+ 13-  0 -4
Curve Equation t Generators 117117bl1 [1,-1,1,-13136,618882] 2 [-770:8319:8]&[-42:1067:1] 117117bl2 [1,-1,1,-213791,38101236] 2 [-364:8403:1]&[231:885:1]
117117bm (2 curves)	0	3- 7- 11+ 13-	-1 3- -2 7- 11+ 13-  0 -4
Curve Equation t 117117bm1 [1,-1,1,45996529,114214367310] 2 117117bm2 [1,-1,1,-259199726,1071065665986] 2
117117bn (2 curves)	0	3- 7- 11+ 13-	-1 3-  4 7- 11+ 13- -6 -4
Curve Equation t 117117bn1 [1,-1,1,-351383,-64714386] 2 117117bn2 [1,-1,1,736132,-386618826] 2
117117bo (1 curve)	0	3- 7- 11+ 13-	2 3-  1 7- 11+ 13-  6 -7
Curve Equation t 117117bo1 [0,0,1,-2847,-413501] 1
117117bp (2 curves)	0	3- 7- 11- 13+	0 3-  0 7- 11- 13+  6 -1
Curve Equation t 117117bp1 [0,0,1,-65910,-6504768] 1 117117bp2 [0,0,1,-263640,45676179] 3
117117bq (4 curves)	0	3- 7- 11- 13+	1 3-  2 7- 11- 13+ -6  4
Curve Equation t 117117bq1 [1,-1,0,15939,-4960760] 2 117117bq2 [1,-1,0,-356706,-77775593] 4 117117bq3 [1,-1,0,-1048761,316003702] 2 117117bq4 [1,-1,0,-5626971,-5136175940] 2
117117br (2 curves)	0	3- 7- 11- 13+	1 3- -2 7- 11- 13+ -4  0
Curve Equation t 117117br1 [1,-1,0,5292,-563549] 2 117117br2 [1,-1,0,-78363,-7774610] 2
117117bs (1 curve)	0	3- 7- 11- 13+	1 3-  3 7- 11- 13+  3  0
Curve Equation t 117117bs1 [1,-1,0,73737,-3767958] 1
117117bt (4 curves)	0	3- 7- 11- 13+	-1 3- -2 7- 11- 13+  2  4
Curve Equation t 117117bt1 [1,-1,1,-23861,11968012] 2 117117bt2 [1,-1,1,-944066,351339616] 4 117117bt3 [1,-1,1,-1529651,-136101338] 2 117117bt4 [1,-1,1,-15081761,22547520766] 2
117117bu (1 curve)	0	3- 7- 11- 13+	-1 3- -4 7- 11- 13+  3 -8
Curve Equation t 117117bu1 [1,-1,1,-32,-1920] 1
117117bv (1 curve)	0	3- 7- 11- 13+	2 3-  2 7- 11- 13+ -6  1
Curve Equation t 117117bv1 [0,0,1,-520550589,3781031112589] 1
117117bw (1 curve)	0	3- 7- 11- 13+	2 3-  4 7- 11- 13+  2 -5
Curve Equation t 117117bw1 [0,0,1,-3393,-56599] 1
117117bx (1 curve)	0	3- 7- 11- 13+	-2 3-  0 7- 11- 13+  2  7
Curve Equation t 117117bx1 [0,0,1,-1285245,558888788] 1
117117by (1 curve)	0	3- 7- 11- 13+	-2 3- -3 7- 11- 13+  8  4
Curve Equation t 117117by1 [0,0,1,-302679,-64791178] 1
117117bz (1 curve)	0	3- 7- 11- 13+	-2 3-  4 7- 11- 13+  2  6
Curve Equation t 117117bz1 [0,0,1,66417,42185146] 1
117117ca (2 curves)	1	3- 7- 11- 13-	1 3-  0 7- 11- 13- -2  4
Curve Equation t Generators 117117ca1 [1,-1,0,-27151227,54460431000] 2 [-332172:15249825:64] 117117ca2 [1,-1,0,-26372592,57730230819] 2 [-2270021124:-102564540327:438976]
117117cb (2 curves)	1	3- 7- 11- 13-	-1 3-  2 7- 11- 13-  2  0
Curve Equation t Generators 117117cb1 [1,-1,1,-149,-412] 2 [46:274:1] 117117cb2 [1,-1,1,436,-3220] 2 [10:40:1]

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