Cremona's table of elliptic curves

117312 = 2⁶ · 3 · 13 · 47

Class	r	Atkin-Lehner	Eigenvalues
117312a (2 curves)	1	2+ 3+ 13+ 47+	2+ 3+  0  0  0 13+ -6  2
Curve Equation t Generators 117312a1 [0,-1,0,-5793,1696545] 2 [159:2184:1] 117312a2 [0,-1,0,-251553,48341793] 2 [-2438:78631:8]
117312b (2 curves)	1	2+ 3+ 13+ 47+	2+ 3+  0  2 -6 13+  3 -2
Curve Equation t Generators 117312b1 [0,-1,0,-3713,99969] 1 [35:108:1] 117312b2 [0,-1,0,25087,-398847] 1 [227:4116:1]
117312c (1 curve)	1	2+ 3+ 13+ 47+	2+ 3+ -1 -3 -2 13+  6  7
Curve Equation t Generators 117312c1 [0,-1,0,-14561,-673503] 1 [321:5256:1]
117312d (1 curve)	0	2+ 3+ 13+ 47-	2+ 3+  0  3 -1 13+  0 -6
Curve Equation t 117312d1 [0,-1,0,-1953,-35295] 1
117312e (4 curves)	0	2+ 3+ 13+ 47-	2+ 3+  2  0 -4 13+  2 -4
Curve Equation t 117312e1 [0,-1,0,668,-27002] 2 117312e2 [0,-1,0,-10377,-373815] 4 117312e3 [0,-1,0,-34817,2075073] 2 117312e4 [0,-1,0,-162657,-25195455] 2
117312f (2 curves)	0	2+ 3+ 13+ 47-	2+ 3+  2  2 -4 13+  6 -6
Curve Equation t 117312f1 [0,-1,0,343,1065] 2 117312f2 [0,-1,0,-1537,10465] 2
117312g (4 curves)	0	2+ 3+ 13+ 47-	2+ 3+ -2 -4  4 13+  2  0
Curve Equation t 117312g1 [0,-1,0,-6470909,6337878573] 2 117312g2 [0,-1,0,-6471089,6337508529] 4 117312g3 [0,-1,0,-5943809,7412632449] 2 117312g4 [0,-1,0,-7001249,5238698913] 2
117312h (1 curve)	0	2+ 3+ 13+ 47-	2+ 3+  3  1 -1 13+  0 -4
Curve Equation t 117312h1 [0,-1,0,-79,-239] 1
117312i (1 curve)	0	2+ 3+ 13+ 47-	2+ 3+  3 -3  3 13+ -6  2
Curve Equation t 117312i1 [0,-1,0,-4709,99261] 1
117312j (1 curve)	0	2+ 3+ 13+ 47-	2+ 3+  4  2 -2 13+ -1 -6
Curve Equation t 117312j1 [0,-1,0,-6241,-188447] 1
117312k (1 curve)	2	2+ 3+ 13- 47+	2+ 3+  0 -3  1 13- -4  2
Curve Equation t Generators 117312k1 [0,-1,0,-3073,76801] 1 [-63:128:1]&[3:260:1]
117312l (4 curves)	0	2+ 3+ 13- 47+	2+ 3+  2  0  0 13-  2 -4
Curve Equation t 117312l1 [0,-1,0,6703,-342063] 2 117312l2 [0,-1,0,-51617,-3642975] 4 117312l3 [0,-1,0,-254657,46264257] 2 117312l4 [0,-1,0,-781697,-265741695] 2
117312m (1 curve)	0	2+ 3+ 13- 47+	2+ 3+ -2 -1  5 13-  6  2
Curve Equation t 117312m1 [0,-1,0,-184449,-32916735] 1
117312n (2 curves)	0	2+ 3+ 13- 47+	2+ 3+ -2  2  0 13-  6  2
Curve Equation t 117312n1 [0,-1,0,-7969,282529] 2 117312n2 [0,-1,0,-128289,17728929] 2
117312o (1 curve)	0	2+ 3+ 13- 47+	2+ 3+  3 -3 -2 13- -2 -7
Curve Equation t 117312o1 [0,-1,0,-449,272001] 1
117312p (1 curve)	0	2+ 3+ 13- 47+	2+ 3+  4  2  6 13-  3  2
Curve Equation t 117312p1 [0,-1,0,316959,441652833] 1
117312q (1 curve)	1	2+ 3+ 13- 47-	2+ 3+ -1  5 -3 13-  4  0
Curve Equation t Generators 117312q1 [0,-1,0,-2711,-39531] 1 [-310:611:8]
117312r (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  1  1  2 13+  6  3
Curve Equation t 117312r1 [0,1,0,-2785,-58753] 1
117312s (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  1  3 -6 13+  2 -3
Curve Equation t 117312s1 [0,1,0,-28705,-2154433] 1
117312t (1 curve)	0	2+ 3- 13+ 47+	2+ 3- -1  3  3 13+ -2  2
Curve Equation t 117312t1 [0,1,0,-2101,-877] 1
117312u (4 curves)	0	2+ 3- 13+ 47+	2+ 3-  2  0  4 13+  2  4
Curve Equation t 117312u1 [0,1,0,668,27002] 2 117312u2 [0,1,0,-10377,373815] 4 117312u3 [0,1,0,-34817,-2075073] 2 117312u4 [0,1,0,-162657,25195455] 2
117312v (2 curves)	0	2+ 3- 13+ 47+	2+ 3-  2 -2  4 13+  6  6
Curve Equation t 117312v1 [0,1,0,343,-1065] 2 117312v2 [0,1,0,-1537,-10465] 2
117312w (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  2 -3 -3 13+ -2  2
Curve Equation t 117312w1 [0,1,0,-864417,-309626433] 1
117312x (1 curve)	2	2+ 3- 13+ 47+	2+ 3- -2 -1 -3 13+  6 -2
Curve Equation t Generators 117312x1 [0,1,0,31,-513] 1 [9:24:1]&[27:144:1]
117312y (2 curves)	2	2+ 3- 13+ 47+	2+ 3- -2 -2 -4 13+ -6  0
Curve Equation t Generators 117312y1 [0,1,0,491,8411] 2 [-10:51:1]&[14:135:1] 117312y2 [0,1,0,-4369,92975] 2 [-73:168:1]&[-22:423:1]
117312z (1 curve)	0	2+ 3- 13+ 47+	2+ 3- -2 -3 -3 13+  2 -6
Curve Equation t 117312z1 [0,1,0,7749791,7795193855] 1
117312ba (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  3 -1  1 13+  0  4
Curve Equation t 117312ba1 [0,1,0,-79,239] 1
117312bb (1 curve)	0	2+ 3- 13+ 47+	2+ 3-  4  5  5 13+ -4  6
Curve Equation t 117312bb1 [0,1,0,15839,1101887] 1
117312bc (1 curve)	0	2+ 3- 13+ 47+	2+ 3- -4  1 -3 13+ -4 -2
Curve Equation t 117312bc1 [0,1,0,69660575,-455466804481] 1
117312bd (1 curve)	1	2+ 3- 13+ 47-	2+ 3-  1 -1 -1 13+  2  6
Curve Equation t Generators 117312bd1 [0,1,0,-12865,556817] 1 [32:423:1]
117312be (1 curve)	1	2+ 3- 13+ 47-	2+ 3- -1  3  2 13+  6 -7
Curve Equation t Generators 117312be1 [0,1,0,-14561,673503] 1 [-89:1128:1]
117312bf (1 curve)	1	2+ 3- 13- 47+	2+ 3- -1 -5  3 13-  4  0
Curve Equation t Generators 117312bf1 [0,1,0,-2711,39531] 1 [42:39:1]
117312bg (4 curves)	1	2+ 3- 13- 47+	2+ 3- -2 -4  0 13- -6 -4
Curve Equation t Generators 117312bg1 [0,1,0,-2449,-47473] 2 [7895:28992:125] 117312bg2 [0,1,0,-2529,-44289] 4 [107:960:1] 117312bg3 [0,1,0,3711,-222753] 2 [778:8265:8] 117312bg4 [0,1,0,-10049,339231] 4 [-83:780:1]
117312bh (1 curve)	1	2+ 3- 13- 47+	2+ 3- -3 -5  2 13-  2 -5
Curve Equation t Generators 117312bh1 [0,1,0,383,3551] 1 [11:-96:1]
117312bi (1 curve)	2	2+ 3- 13- 47-	2+ 3-  0 -1 -5 13-  4 -2
Curve Equation t Generators 117312bi1 [0,1,0,-12057793,16111712927] 1 [-1141:168480:1]&[-439:146016:1]
117312bj (4 curves)	0	2+ 3- 13- 47-	2+ 3- -2  0  0 13- -6  4
Curve Equation t 117312bj1 [0,1,0,-3809,59007] 2 117312bj2 [0,1,0,-24289,-1419649] 4 117312bj3 [0,1,0,8991,-4980609] 4 117312bj4 [0,1,0,-385249,-92164993] 2
117312bk (1 curve)	2	2+ 3- 13- 47-	2+ 3- -2 -1  3 13- -6 -6
Curve Equation t Generators 117312bk1 [0,1,0,52671,4787487] 1 [219:5184:1]&[-51:1404:1]
117312bl (1 curve)	0	2+ 3- 13- 47-	2+ 3-  3  3  2 13- -2  7
Curve Equation t 117312bl1 [0,1,0,-449,-272001] 1
117312bm (1 curve)	2	2+ 3- 13- 47-	2+ 3- -3 -1 -5 13- -2 -2
Curve Equation t Generators 117312bm1 [0,1,0,-137,-639] 1 [-8:3:1]&[16:39:1]
117312bn (1 curve)	0	2+ 3- 13- 47-	2+ 3-  4  3  3 13-  0 -2
Curve Equation t 117312bn1 [0,1,0,2879,32927] 1
117312bo (1 curve)	0	2- 3+ 13+ 47+	2- 3+  0 -2 -2 13+  3 -6
Curve Equation t 117312bo1 [0,-1,0,-3056353,4268927905] 1
117312bp (1 curve)	0	2- 3+ 13+ 47+	2- 3+  1  1  1 13+  2 -6
Curve Equation t 117312bp1 [0,-1,0,-12865,-556817] 1
117312bq (1 curve)	0	2- 3+ 13+ 47+	2- 3+  1 -3  5 13+  0  0
Curve Equation t 117312bq1 [0,-1,0,-94115,11141253] 1
117312br (1 curve)	1	2- 3+ 13+ 47-	2- 3+  0 -3 -5 13+ -8  2
Curve Equation t Generators 117312br1 [0,-1,0,-241788,123845346] 1 [275:8836:1]
117312bs (1 curve)	1	2- 3+ 13+ 47-	2- 3+  1 -1 -2 13+  6 -3
Curve Equation t Generators 117312bs1 [0,-1,0,-2785,58753] 1 [-51:256:1]
117312bt (1 curve)	1	2- 3+ 13+ 47-	2- 3+  1 -3  6 13+  2  3
Curve Equation t Generators 117312bt1 [0,-1,0,-28705,2154433] 1 [189:1856:1]
117312bu (1 curve)	1	2- 3+ 13+ 47-	2- 3+ -1 -3 -3 13+ -2 -2
Curve Equation t Generators 117312bu1 [0,-1,0,-2101,877] 1 [-36:169:1]
117312bv (1 curve)	1	2- 3+ 13+ 47-	2- 3+  2  3  3 13+ -2 -2
Curve Equation t Generators 117312bv1 [0,-1,0,-864417,309626433] 1 [6251:489004:1]
117312bw (1 curve)	1	2- 3+ 13+ 47-	2- 3+ -2  1  3 13+  6  2
Curve Equation t Generators 117312bw1 [0,-1,0,31,513] 1 [7:32:1]
117312bx (2 curves)	1	2- 3+ 13+ 47-	2- 3+ -2  2  4 13+ -6  0
Curve Equation t Generators 117312bx1 [0,-1,0,491,-8411] 2 [23694:251281:216] 117312bx2 [0,-1,0,-4369,-92975] 2 [443:9204:1]
117312by (1 curve)	1	2- 3+ 13+ 47-	2- 3+ -2  3  3 13+  2  6
Curve Equation t Generators 117312by1 [0,-1,0,7749791,-7795193855] 1 [2282631:81529772:2197]
117312bz (2 curves)	1	2- 3+ 13+ 47-	2- 3+  4  2  0 13+  2  6
Curve Equation t Generators 117312bz1 [0,-1,0,-35816,2110038] 2 [-6924414:-159458545:74088] 117312bz2 [0,-1,0,-179401,-27324887] 2 [-13522792014690:-68816562478847:63521199000]
117312ca (1 curve)	1	2- 3+ 13+ 47-	2- 3+  4 -5 -5 13+ -4 -6
Curve Equation t Generators 117312ca1 [0,-1,0,15839,-1101887] 1 [267:4700:1]
117312cb (1 curve)	1	2- 3+ 13+ 47-	2- 3+ -4 -1  3 13+ -4  2
Curve Equation t Generators 117312cb1 [0,-1,0,69660575,455466804481] 1 [-2156016143197413937776975:336414900770129386240113116:718324333571101160051]
117312cc (1 curve)	1	2- 3+ 13- 47+	2- 3+  0  1  5 13-  4  2
Curve Equation t Generators 117312cc1 [0,-1,0,-12057793,-16111712927] 1 [20793949347:76938647680:5177717]
117312cd (1 curve)	1	2- 3+ 13- 47+	2- 3+  0  2  2 13- -5  6
Curve Equation t Generators 117312cd1 [0,-1,0,-33,-639] 1 [27:132:1]
117312ce (4 curves)	1	2- 3+ 13- 47+	2- 3+ -2  0  0 13- -6 -4
Curve Equation t Generators 117312ce1 [0,-1,0,-3809,-59007] 2 [-246:1341:8] 117312ce2 [0,-1,0,-24289,1419649] 4 [-85:1692:1] 117312ce3 [0,-1,0,8991,4980609] 2 [576:14175:1] 117312ce4 [0,-1,0,-385249,92164993] 4 [683:12132:1]
117312cf (1 curve)	1	2- 3+ 13- 47+	2- 3+ -2  1 -3 13- -6  6
Curve Equation t Generators 117312cf1 [0,-1,0,52671,-4787487] 1 [311:6448:1]
117312cg (1 curve)	1	2- 3+ 13- 47+	2- 3+ -3  1  5 13- -2  2
Curve Equation t Generators 117312cg1 [0,-1,0,-137,639] 1 [10:13:1]
117312ch (1 curve)	1	2- 3+ 13- 47+	2- 3+  4 -3 -3 13-  0  2
Curve Equation t Generators 117312ch1 [0,-1,0,2879,-32927] 1 [2247:106520:1]
117312ci (1 curve)	1	2- 3+ 13- 47+	2- 3+ -4 -1 -3 13-  0  2
Curve Equation t Generators 117312ci1 [0,-1,0,-20,-54] 1 [7:10:1]
117312cj (1 curve)	0	2- 3+ 13- 47-	2- 3+ -1  5  3 13-  4  4
Curve Equation t 117312cj1 [0,-1,0,-611,5997] 1
117312ck (4 curves)	0	2- 3+ 13- 47-	2- 3+ -2  4  0 13- -6  4
Curve Equation t 117312ck1 [0,-1,0,-2449,47473] 2 117312ck2 [0,-1,0,-2529,44289] 4 117312ck3 [0,-1,0,3711,222753] 4 117312ck4 [0,-1,0,-10049,-339231] 2
117312cl (1 curve)	0	2- 3+ 13- 47-	2- 3+ -3  5 -2 13-  2  5
Curve Equation t 117312cl1 [0,-1,0,383,-3551] 1
117312cm (1 curve)	1	2- 3- 13+ 47+	2- 3-  0  3  5 13+ -8 -2
Curve Equation t Generators 117312cm1 [0,1,0,-241788,-123845346] 1 [83085:23948532:1]
117312cn (1 curve)	1	2- 3- 13+ 47+	2- 3-  0 -3  1 13+  0  6
Curve Equation t Generators 117312cn1 [0,1,0,-1953,35295] 1 [-43:204:1]
117312co (4 curves)	1	2- 3- 13+ 47+	2- 3- -2  4 -4 13+  2  0
Curve Equation t Generators 117312co1 [0,1,0,-6470909,-6337878573] 2 [-29931599650554602:2003942196777:20375497153297] 117312co2 [0,1,0,-6471089,-6337508529] 4 [47427080383665355619145614:-16961609133054385994193825357:370659776562853250759] 117312co3 [0,1,0,-5943809,-7412632449] 2 [167033089211762408459109769817639427761995178100420282459867:-3109166069408399207440109936342511731782649639541851073715220:54424115119698496606344928358244796747805722047874365951] 117312co4 [0,1,0,-7001249,-5238698913] 2 [-17309708849310643803:-141867146522560473872:20621993124535083]
117312cp (1 curve)	1	2- 3- 13+ 47+	2- 3-  3  3 -3 13+ -6 -2
Curve Equation t Generators 117312cp1 [0,1,0,-4709,-99261] 1 [-50:117:1]
117312cq (2 curves)	1	2- 3- 13+ 47+	2- 3-  4 -2  0 13+  2 -6
Curve Equation t Generators 117312cq1 [0,1,0,-35816,-2110038] 2 [1153:38610:1] 117312cq2 [0,1,0,-179401,27324887] 2 [-382:6345:1]
117312cr (1 curve)	1	2- 3- 13+ 47+	2- 3-  4 -2  2 13+ -1  6
Curve Equation t Generators 117312cr1 [0,1,0,-6241,188447] 1 [23:240:1]
117312cs (2 curves)	0	2- 3- 13+ 47-	2- 3-  0  0  0 13+ -6 -2
Curve Equation t 117312cs1 [0,1,0,-5793,-1696545] 2 117312cs2 [0,1,0,-251553,-48341793] 2
117312ct (1 curve)	0	2- 3- 13+ 47-	2- 3-  0  2  2 13+  3  6
Curve Equation t 117312ct1 [0,1,0,-3056353,-4268927905] 1
117312cu (2 curves)	0	2- 3- 13+ 47-	2- 3-  0 -2  6 13+  3  2
Curve Equation t 117312cu1 [0,1,0,-3713,-99969] 1 117312cu2 [0,1,0,25087,398847] 1
117312cv (1 curve)	0	2- 3- 13+ 47-	2- 3-  1  3 -5 13+  0  0
Curve Equation t 117312cv1 [0,1,0,-94115,-11141253] 1
117312cw (1 curve)	2	2- 3- 13- 47+	2- 3- -1 -5 -3 13-  4 -4
Curve Equation t Generators 117312cw1 [0,1,0,-611,-5997] 1 [-14:3:1]&[34:117:1]
117312cx (1 curve)	1	2- 3- 13- 47-	2- 3-  0 -2 -2 13- -5 -6
Curve Equation t Generators 117312cx1 [0,1,0,-33,639] 1 [3:-24:1]
117312cy (1 curve)	1	2- 3- 13- 47-	2- 3-  0  3 -1 13- -4 -2
Curve Equation t Generators 117312cy1 [0,1,0,-3073,-76801] 1 [65:48:1]
117312cz (4 curves)	1	2- 3- 13- 47-	2- 3-  2  0  0 13-  2  4
Curve Equation t Generators 117312cz1 [0,1,0,6703,342063] 2 [7:624:1] 117312cz2 [0,1,0,-51617,3642975] 4 [-107:2820:1] 117312cz3 [0,1,0,-254657,-46264257] 2 [-251:1380:1] 117312cz4 [0,1,0,-781697,265741695] 2 [2863:-146640:1]
117312da (1 curve)	1	2- 3- 13- 47-	2- 3- -2  1 -5 13-  6 -2
Curve Equation t Generators 117312da1 [0,1,0,-184449,32916735] 1 [-123:7332:1]
117312db (2 curves)	1	2- 3- 13- 47-	2- 3- -2 -2  0 13-  6 -2
Curve Equation t Generators 117312db1 [0,1,0,-7969,-282529] 2 [272053395:14860680704:91125] 117312db2 [0,1,0,-128289,-17728929] 2 [11943:1304640:1]
117312dc (1 curve)	1	2- 3- 13- 47-	2- 3-  4 -2 -6 13-  3 -2
Curve Equation t Generators 117312dc1 [0,1,0,316959,-441652833] 1 [277809:6389760:343]
117312dd (1 curve)	1	2- 3- 13- 47-	2- 3- -4  1  3 13-  0 -2
Curve Equation t Generators 117312dd1 [0,1,0,-20,54] 1 [1:6:1]

Data from Elliptic Curve Data by J. E. Cremona.
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