Cremona's table of elliptic curves

15600 = 2⁴ · 3 · 5² · 13

Class	r	Atkin-Lehner	Eigenvalues
15600a (4 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  0  0 13+  6 -4
Curve Equation t Generators 15600a1 [0,-1,0,4217,-8438] 2 [5478:126064:1331] 15600a2 [0,-1,0,-16908,-50688] 4 [-124:352:1] 15600a3 [0,-1,0,-192408,-32342688] 2 [-133688:83699:512] 15600a4 [0,-1,0,-179408,29199312] 2 [-472:2916:1]
15600b (6 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  0  4 13+ -2  4
Curve Equation t Generators 15600b1 [0,-1,0,-232383,-46589238] 2 [5017257030552895722589342:-629663582763707177687408924:318231343713856238639] 15600b2 [0,-1,0,-3802508,-2852707488] 4 [-54576164007236:-3150150746072:48587168449] 15600b3 [0,-1,0,-60840008,-182634907488] 2 [-260565260977735856848985900362:4972734025601951898998951:57864819526708515785780408] 15600b4 [0,-1,0,-3887008,-2719197488] 4 [10171722:856237850:1331] 15600b5 [0,-1,0,-13364008,15704090512] 2 [1096:48708:1] 15600b6 [0,-1,0,4237992,-12599197488] 2 [6991579449118:617164980939150:938313739]
15600c (1 curve)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  0  4 13+ -8 -5
Curve Equation t Generators 15600c1 [0,-1,0,-5208,-191088] 1 [88:156:1]
15600d (4 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  0 -4 13+  2  4
Curve Equation t Generators 15600d1 [0,-1,0,2092,-26688] 2 [76:752:1] 15600d2 [0,-1,0,-10408,-226688] 4 [-48:400:1] 15600d3 [0,-1,0,-145408,-21286688] 2 [453:2366:1] 15600d4 [0,-1,0,-75408,7833312] 2 [277:2850:1]
15600e (4 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  4  0 13+ -2 -8
Curve Equation t Generators 15600e1 [0,-1,0,-983,-11538] 2 [3748:22925:64] 15600e2 [0,-1,0,-1108,-8288] 4 [-12:56:1] 15600e3 [0,-1,0,-7608,251712] 2 [-24:648:1] 15600e4 [0,-1,0,3392,-62288] 2 [22:150:1]
15600f (4 curves)	1	2+ 3+ 5+ 13+	2+ 3+ 5+  4 -4 13+ -6  0
Curve Equation t Generators 15600f1 [0,-1,0,-508,-15488] 2 [228:3416:1] 15600f2 [0,-1,0,-13008,-565488] 4 [-64:28:1] 15600f3 [0,-1,0,-208008,-36445488] 2 [962:25550:1] 15600f4 [0,-1,0,-18008,-85488] 2 [-88:900:1]
15600g (1 curve)	1	2+ 3+ 5+ 13+	2+ 3+ 5+ -5 -1 13+  3 -6
Curve Equation t Generators 15600g1 [0,-1,0,-8633,311637] 1 [52:25:1]
15600h (2 curves)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  0  2 13- -2 -8
Curve Equation t 15600h1 [0,-1,0,-16283,-745938] 2 15600h2 [0,-1,0,14092,-3236688] 2
15600i (2 curves)	0	2+ 3+ 5+ 13-	2+ 3+ 5+  2 -4 13-  0 -2
Curve Equation t 15600i1 [0,-1,0,17992,976512] 2 15600i2 [0,-1,0,-107008,9476512] 2
15600j (2 curves)	0	2+ 3+ 5+ 13-	2+ 3+ 5+ -4  2 13-  6  4
Curve Equation t 15600j1 [0,-1,0,-83,162] 2 15600j2 [0,-1,0,292,912] 2
15600k (1 curve)	0	2+ 3+ 5- 13+	2+ 3+ 5- -1 -3 13+ -7  0
Curve Equation t 15600k1 [0,-1,0,-6113,-182403] 1
15600l (1 curve)	1	2+ 3+ 5- 13-	2+ 3+ 5-  5 -5 13- -3  4
Curve Equation t Generators 15600l1 [0,-1,0,47,2077] 1 [12:65:1]
15600m (4 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+  0  0 13+ -2  4
Curve Equation t 15600m1 [0,1,0,-183,-612] 2 15600m2 [0,1,0,-1308,17388] 4 15600m3 [0,1,0,-20808,1148388] 2 15600m4 [0,1,0,192,56388] 2
15600n (1 curve)	0	2+ 3- 5+ 13+	2+ 3- 5+ -1  5 13+ -3  6
Curve Equation t 15600n1 [0,1,0,242967,-30253437] 1
15600o (2 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+ -2  0 13+  4 -6
Curve Equation t 15600o1 [0,1,0,-8,-6012] 2 15600o2 [0,1,0,-5008,-136012] 2
15600p (4 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+  4  0 13+ -2  0
Curve Equation t 15600p1 [0,1,0,-57383,4441488] 2 15600p2 [0,1,0,-877508,316088988] 4 15600p3 [0,1,0,-14040008,20244113988] 2 15600p4 [0,1,0,-837008,346625988] 2
15600q (4 curves)	0	2+ 3- 5+ 13+	2+ 3- 5+ -4 -4 13+  6  0
Curve Equation t 15600q1 [0,1,0,-2783,-57312] 2 15600q2 [0,1,0,-3908,-7812] 4 15600q3 [0,1,0,-41408,3217188] 2 15600q4 [0,1,0,15592,-46812] 2
15600r (4 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+  0  0 13- -2  0
Curve Equation t Generators 15600r1 [0,1,0,-121908,-16423812] 2 [6198:487200:1] 15600r2 [0,1,0,-122408,-16282812] 4 [-221:156:1] 15600r3 [0,1,0,-247408,22467188] 4 [-532:1950:1] 15600r4 [0,1,0,-5408,-46000812] 2 [379:2556:1]
15600s (2 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+  0 -6 13- -2  0
Curve Equation t Generators 15600s1 [0,1,0,-83,588] 2 [24:114:1] 15600s2 [0,1,0,-1708,26588] 2 [22:12:1]
15600t (1 curve)	1	2+ 3- 5+ 13-	2+ 3- 5+ -3  3 13-  1  6
Curve Equation t Generators 15600t1 [0,1,0,-2633,-80637] 1 [118:1125:1]
15600u (2 curves)	1	2+ 3- 5+ 13-	2+ 3- 5+ -4  2 13-  6 -4
Curve Equation t Generators 15600u1 [0,1,0,117,-1512] 2 [12:42:1] 15600u2 [0,1,0,-1508,-21012] 2 [-26:36:1]
15600v (1 curve)	1	2+ 3- 5- 13+	2+ 3- 5- -5 -5 13+  3  4
Curve Equation t Generators 15600v1 [0,1,0,1167,261963] 1 [-42:375:1]
15600w (1 curve)	0	2+ 3- 5- 13-	2+ 3- 5-  0  4 13-  8 -5
Curve Equation t 15600w1 [0,1,0,-208,-1612] 1
15600x (1 curve)	0	2+ 3- 5- 13-	2+ 3- 5-  1 -3 13-  7  0
Curve Equation t 15600x1 [0,1,0,-152833,-23106037] 1
15600y (1 curve)	0	2- 3+ 5+ 13+	2- 3+ 5+  0 -4 13+  0 -1
Curve Equation t 15600y1 [0,-1,0,-143848,22352752] 1
15600z (6 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  0 -4 13+  6 -4
Curve Equation t 15600z1 [0,-1,0,5992,-73488] 2 15600z2 [0,-1,0,-26008,-585488] 4 15600z3 [0,-1,0,-338008,-75465488] 2 15600z4 [0,-1,0,-226008,41014512] 4 15600z5 [0,-1,0,-3606008,2636854512] 2 15600z6 [0,-1,0,-46008,104374512] 2
15600ba (2 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+ -2  4 13+ -2  2
Curve Equation t 15600ba1 [0,-1,0,-133,-488] 2 15600ba2 [0,-1,0,-508,4012] 2
15600bb (1 curve)	0	2- 3+ 5+ 13+	2- 3+ 5+  3 -1 13+  3  2
Curve Equation t 15600bb1 [0,-1,0,4867,24487137] 1
15600bc (1 curve)	0	2- 3+ 5+ 13+	2- 3+ 5+  3 -1 13+ -3 -4
Curve Equation t 15600bc1 [0,-1,0,-68,-228] 1
15600bd (4 curves)	0	2- 3+ 5+ 13+	2- 3+ 5+  4  4 13+ -2  8
Curve Equation t 15600bd1 [0,-1,0,-7808,-5541888] 2 15600bd2 [0,-1,0,-519808,-142757888] 4 15600bd3 [0,-1,0,-8295808,-9194021888] 2 15600bd4 [0,-1,0,-935808,118490112] 2
15600be (4 curves)	2	2- 3+ 5+ 13+	2- 3+ 5+ -4 -4 13+ -2  0
Curve Equation t Generators 15600be1 [0,-1,0,192,2112] 2 [2:50:1]&[8:64:1] 15600be2 [0,-1,0,-1808,26112] 4 [-32:224:1]&[-22:234:1] 15600be3 [0,-1,0,-7808,-237888] 2 [-59:118:1]&[-38:50:1] 15600be4 [0,-1,0,-27808,1794112] 2 [-128:1800:1]&[72:400:1]
15600bf (4 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+  0  0 13-  6  0
Curve Equation t Generators 15600bf1 [0,-1,0,-5408,-146688] 2 [-38:50:1] 15600bf2 [0,-1,0,-13408,397312] 4 [16:432:1] 15600bf3 [0,-1,0,-193408,32797312] 4 [-328:7800:1] 15600bf4 [0,-1,0,38592,2685312] 2 [666:17982:1]
15600bg (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+ -1  5 13- -5  0
Curve Equation t Generators 15600bg1 [0,-1,0,-13208,-580368] 1 [1106:36558:1]
15600bh (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+  2 -4 13- -8  6
Curve Equation t Generators 15600bh1 [0,-1,0,1592,67312] 2 [-3:250:1] 15600bh2 [0,-1,0,-18408,867312] 2 [-78:1350:1]
15600bi (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+ -2  2 13-  2  2
Curve Equation t Generators 15600bi1 [0,-1,0,-2633,-50988] 2 [-3820:184:125] 15600bi2 [0,-1,0,-1508,-95988] 2 [137:1500:1]
15600bj (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+ -2 -4 13- -4  2
Curve Equation t Generators 15600bj1 [0,-1,0,-21008,1240512] 2 [82:250:1] 15600bj2 [0,-1,0,-341008,76760512] 2 [312:800:1]
15600bk (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+  3  1 13-  1  2
Curve Equation t Generators 15600bk1 [0,-1,0,-76133,-8277363] 1 [532:10075:1]
15600bl (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+  3  1 13- -5  8
Curve Equation t Generators 15600bl1 [0,-1,0,-728,8112] 1 [26:78:1]
15600bm (2 curves)	1	2- 3+ 5+ 13-	2- 3+ 5+ -3  3 13-  3  0
Curve Equation t Generators 15600bm1 [0,-1,0,-5684848,5717413312] 1 [-182:82134:1] 15600bm2 [0,-1,0,-3646500208,84755659198912] 1 [4356770:412158:125]
15600bn (1 curve)	1	2- 3+ 5+ 13-	2- 3+ 5+  4 -4 13- -4 -7
Curve Equation t Generators 15600bn1 [0,-1,0,32,-128] 1 [8:24:1]
15600bo (2 curves)	1	2- 3+ 5- 13+	2- 3+ 5-  0  6 13+  0 -6
Curve Equation t Generators 15600bo1 [0,-1,0,-248,1392] 2 [-4:48:1] 15600bo2 [0,-1,0,-1048,-11408] 2 [-14:18:1]
15600bp (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5-  1  1 13+ -1  4
Curve Equation t Generators 15600bp1 [0,-1,0,-53,-1923] 1 [52:365:1]
15600bq (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5-  1  1 13+ -7  0
Curve Equation t Generators 15600bq1 [0,-1,0,192,-7488] 1 [42:270:1]
15600br (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5- -1  3 13+  1  8
Curve Equation t Generators 15600br1 [0,-1,0,792,-83088] 1 [42:150:1]
15600bs (2 curves)	1	2- 3+ 5- 13+	2- 3+ 5- -2 -2 13+  2  4
Curve Equation t Generators 15600bs1 [0,-1,0,15792,126912] 2 [56:1088:1] 15600bs2 [0,-1,0,-64208,1086912] 2 [-152:2704:1]
15600bt (1 curve)	1	2- 3+ 5- 13+	2- 3+ 5-  3 -3 13+ -3  0
Curve Equation t Generators 15600bt1 [0,-1,0,-1515333,730668537] 1 [2317:98250:1]
15600bu (2 curves)	1	2- 3+ 5- 13+	2- 3+ 5-  4 -2 13+ -4 -2
Curve Equation t Generators 15600bu1 [0,-1,0,-3559208,2585676912] 2 [-2044:36288:1] 15600bu2 [0,-1,0,-3639208,2463436912] 2 [77442:21544250:1]
15600bv (2 curves)	0	2- 3+ 5- 13-	2- 3+ 5-  1  3 13-  3  4
Curve Equation t 15600bv1 [0,-1,0,-40708,-16727588] 1 15600bv2 [0,-1,0,364292,437682412] 1
15600bw (1 curve)	0	2- 3+ 5- 13-	2- 3+ 5-  1  3 13- -7  4
Curve Equation t 15600bw1 [0,-1,0,-1333,-19463] 1
15600bx (2 curves)	0	2- 3+ 5- 13-	2- 3+ 5-  4  0 13-  0 -5
Curve Equation t 15600bx1 [0,-1,0,4792,2748912] 1 15600bx2 [0,-1,0,-1345208,601068912] 1
15600by (2 curves)	0	2- 3+ 5- 13-	2- 3+ 5-  4  6 13- -4 -2
Curve Equation t 15600by1 [0,-1,0,-5168,4032] 2 15600by2 [0,-1,0,-56368,-5115968] 2
15600bz (8 curves)	1	2- 3- 5+ 13+	2- 3- 5+  0 -4 13+ -2  4
Curve Equation t Generators 15600bz1 [0,1,0,-44008,-3568012] 2 [-121:6:1] 15600bz2 [0,1,0,-46008,-3228012] 4 [-132:750:1] 15600bz3 [0,1,0,-208008,33383988] 4 [78:4200:1] 15600bz4 [0,1,0,83992,-18048012] 2 [388:8550:1] 15600bz5 [0,1,0,-3250008,2254043988] 4 [1092:2898:1] 15600bz6 [0,1,0,241992,158483988] 2 [828:30450:1] 15600bz7 [0,1,0,-52000008,144311543988] 2 [50661364:1134966:12167] 15600bz8 [0,1,0,-3172008,2367455988] 2 [21684:496846:27]
15600ca (2 curves)	1	2- 3- 5+ 13+	2- 3- 5+ -1  3 13+ -3  4
Curve Equation t Generators 15600ca1 [0,1,0,-1628,-134472] 1 [79:486:1] 15600ca2 [0,1,0,14572,3507288] 1 [-41:1686:1]
15600cb (2 curves)	1	2- 3- 5+ 13+	2- 3- 5+ -1 -3 13+ -3 -2
Curve Equation t Generators 15600cb1 [0,1,0,467,-937] 1 [23:150:1] 15600cb2 [0,1,0,-5533,179063] 1 [43:150:1]
15600cc (4 curves)	1	2- 3- 5+ 13+	2- 3- 5+  2  0 13+  0 -2
Curve Equation t Generators 15600cc1 [0,1,0,-2408,-292812] 2 [103:750:1] 15600cc2 [0,1,0,-82408,-9092812] 2 [-172:150:1] 15600cc3 [0,1,0,21592,7723188] 2 [19146:526400:27] 15600cc4 [0,1,0,-478408,120723188] 2 [-412:15750:1]
15600cd (4 curves)	1	2- 3- 5+ 13+	2- 3- 5+  2  0 13+  0 -2
Curve Equation t Generators 15600cd1 [0,1,0,1598992,-28788012] 2 [274:20736:1] 15600cd2 [0,1,0,-6401008,-236788012] 2 [-2062:64800:1] 15600cd3 [0,1,0,-21351008,40954511988] 2 [6868:467250:1] 15600cd4 [0,1,0,-349031008,2509695631988] 2 [-262:1612800:1]
15600ce (4 curves)	1	2- 3- 5+ 13+	2- 3- 5+  2  0 13+  6 -2
Curve Equation t Generators 15600ce1 [0,1,0,-333,-162] 2 [-18:18:1] 15600ce2 [0,1,0,-3708,-87912] 2 [1263:44850:1] 15600ce3 [0,1,0,-18333,949338] 2 [-118:1218:1] 15600ce4 [0,1,0,-18708,908088] 2 [-324842:3335667:2744]
15600cf (1 curve)	1	2- 3- 5+ 13+	2- 3- 5+ -3  5 13+ -5 -2
Curve Equation t Generators 15600cf1 [0,1,0,-133,5363] 1 [-2:75:1]
15600cg (2 curves)	1	2- 3- 5+ 13+	2- 3- 5+ -4  0 13+  0 -5
Curve Equation t Generators 15600cg1 [0,1,0,192,22068] 1 [-6:144:1] 15600cg2 [0,1,0,-53808,4787028] 1 [114:384:1]
15600ch (1 curve)	0	2- 3- 5+ 13-	2- 3- 5+  1  3 13- -1  8
Curve Equation t 15600ch1 [0,1,0,32,-652] 1
15600ci (1 curve)	0	2- 3- 5+ 13-	2- 3- 5+ -1  1 13-  7  0
Curve Equation t 15600ci1 [0,1,0,4792,-926412] 1
15600cj (1 curve)	0	2- 3- 5+ 13-	2- 3- 5+ -1 -5 13-  7  6
Curve Equation t 15600cj1 [0,1,0,-26533,2604563] 1
15600ck (2 curves)	0	2- 3- 5+ 13-	2- 3- 5+ -2  6 13-  2  2
Curve Equation t 15600ck1 [0,1,0,-2033,-4062] 2 15600ck2 [0,1,0,8092,-24312] 2
15600cl (4 curves)	0	2- 3- 5+ 13-	2- 3- 5+  4  0 13-  2 -4
Curve Equation t 15600cl1 [0,1,0,-115408,-24968812] 2 15600cl2 [0,1,0,-2163408,-1225096812] 4 15600cl3 [0,1,0,-34611408,-78386440812] 2 15600cl4 [0,1,0,-2483408,-839176812] 4
15600cm (1 curve)	0	2- 3- 5- 13+	2- 3- 5-  1  5 13+  5  0
Curve Equation t 15600cm1 [0,1,0,-330208,-73206412] 1
15600cn (1 curve)	0	2- 3- 5- 13+	2- 3- 5- -1  3 13+  7  4
Curve Equation t 15600cn1 [0,1,0,-53,-177] 1
15600co (2 curves)	0	2- 3- 5- 13+	2- 3- 5-  3  3 13+ -3  0
Curve Equation t 15600co1 [0,1,0,-145860008,677986929588] 1 15600co2 [0,1,0,-142121208,714392421588] 1
15600cp (1 curve)	0	2- 3- 5- 13+	2- 3- 5- -3  1 13+  5  8
Curve Equation t 15600cp1 [0,1,0,-18208,977588] 1
15600cq (1 curve)	0	2- 3- 5- 13+	2- 3- 5- -4 -4 13+  4 -7
Curve Equation t 15600cq1 [0,1,0,792,-14412] 1
15600cr (2 curves)	0	2- 3- 5- 13+	2- 3- 5- -4  6 13+  4 -2
Curve Equation t 15600cr1 [0,1,0,-129208,245588] 2 15600cr2 [0,1,0,-1409208,-642314412] 2
15600cs (1 curve)	1	2- 3- 5- 13-	2- 3- 5-  0 -4 13-  0 -1
Curve Equation t Generators 15600cs1 [0,1,0,-3596208,2786901588] 1 [1842:49152:1]
15600ct (2 curves)	1	2- 3- 5- 13-	2- 3- 5-  0  6 13-  0 -6
Curve Equation t Generators 15600ct1 [0,1,0,-6208,161588] 2 [74:336:1] 15600ct2 [0,1,0,-26208,-1478412] 2 [-78:312:1]
15600cu (1 curve)	1	2- 3- 5- 13-	2- 3- 5- -1  1 13-  1  4
Curve Equation t Generators 15600cu1 [0,1,0,-1333,-243037] 1 [158:1875:1]
15600cv (2 curves)	1	2- 3- 5- 13-	2- 3- 5-  2 -2 13- -2  4
Curve Equation t Generators 15600cv1 [0,1,0,632,1268] 2 [7:78:1] 15600cv2 [0,1,0,-2568,7668] 2 [-36:234:1]
15600cw (1 curve)	1	2- 3- 5- 13-	2- 3- 5- -3 -1 13-  3 -4
Curve Equation t Generators 15600cw1 [0,1,0,-1708,-31912] 1 [59:276:1]
15600cx (1 curve)	1	2- 3- 5- 13-	2- 3- 5- -3 -3 13-  3  0
Curve Equation t Generators 15600cx1 [0,1,0,-60613,5821103] 1 [83:1170:1]
15600cy (2 curves)	1	2- 3- 5- 13-	2- 3- 5- -4 -2 13-  4 -2
Curve Equation t Generators 15600cy1 [0,1,0,-142368,20628468] 2 [228:270:1] 15600cy2 [0,1,0,-145568,19649268] 2 [-86:5616:1]

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations