Cremona's table of elliptic curves

70720 = 2⁶ · 5 · 13 · 17

Class	r	Atkin-Lehner	Eigenvalues
70720a (2 curves)	1	2+ 5+ 13+ 17+	2+  0 5+  4  2 13+ 17+  4
Curve Equation t Generators 70720a1 [0,0,0,-428,-848] 2 [-18:32:1] 70720a2 [0,0,0,1652,-6672] 2 [8:84:1]
70720b (4 curves)	1	2+ 5+ 13+ 17+	2+  2 5+  2  0 13+ 17+  4
Curve Equation t Generators 70720b1 [0,-1,0,-354721,81434145] 2 [-231:12288:1] 70720b2 [0,-1,0,-363041,77422241] 2 [-6315:330112:27] 70720b3 [0,-1,0,-538721,-11591455] 2 [-114011327:-4279812096:389017] 70720b4 [0,-1,0,-6163041,-5873257759] 2 [-1701193859683395:-596271061234304:1235721447891]
70720c (2 curves)	1	2+ 5+ 13+ 17+	2+  2 5+  4  0 13+ 17+ -2
Curve Equation t Generators 70720c1 [0,-1,0,-261,-1435] 2 [407832:1730575:13824] 70720c2 [0,-1,0,239,-6735] 2 [2901:30160:27]
70720d (2 curves)	1	2+ 5+ 13+ 17+	2+ -2 5+ -2  4 13+ 17+  4
Curve Equation t Generators 70720d1 [0,1,0,-142561,-20488065] 2 [-215:520:1] 70720d2 [0,1,0,-2272481,-1319313281] 2 [14282:142375:8]
70720e (2 curves)	2	2+ 5+ 13+ 17-	2+  0 5+ -2  0 13+ 17- -2
Curve Equation t Generators 70720e1 [0,0,0,-1468,21648] 2 [-42:96:1]&[13:69:1] 70720e2 [0,0,0,-1388,24112] 2 [-18:208:1]&[21:65:1]
70720f (4 curves)	0	2+ 5+ 13+ 17-	2+  0 5+ -4  0 13+ 17-  4
Curve Equation t 70720f1 [0,0,0,-101228,12280752] 2 70720f2 [0,0,0,-183148,-10427472] 4 70720f3 [0,0,0,682132,-80688208] 2 70720f4 [0,0,0,-2359148,-1393493072] 2
70720g (2 curves)	2	2+ 5+ 13+ 17-	2+ -2 5+ -4 -2 13+ 17-  2
Curve Equation t Generators 70720g1 [0,1,0,-25041,1516879] 2 [-165:1088:1]&[90:17:1] 70720g2 [0,1,0,-24961,1527135] 2 [-115:1700:1]&[-13:1360:1]
70720h (2 curves)	0	2+ 5+ 13- 17+	2+  0 5+  0  6 13- 17+  0
Curve Equation t 70720h1 [0,0,0,-11948,-427728] 2 70720h2 [0,0,0,21332,-2384592] 2
70720i (2 curves)	0	2+ 5+ 13- 17+	2+  0 5+  2 -2 13- 17+ -2
Curve Equation t 70720i1 [0,0,0,277,1172] 2 70720i2 [0,0,0,-1348,10272] 2
70720j (2 curves)	0	2+ 5+ 13- 17+	2+  0 5+ -2  2 13- 17+  2
Curve Equation t 70720j1 [0,0,0,277,-1172] 2 70720j2 [0,0,0,-1348,-10272] 2
70720k (2 curves)	0	2+ 5+ 13- 17+	2+  2 5+ -2  0 13- 17+ -4
Curve Equation t 70720k1 [0,-1,0,-23041,842241] 2 70720k2 [0,-1,0,-156161,-23092735] 2
70720l (2 curves)	0	2+ 5- 13+ 17+	2+  2 5-  0  0 13+ 17+  2
Curve Equation t 70720l1 [0,-1,0,-40,450] 2 70720l2 [0,-1,0,-1145,15257] 2
70720m (4 curves)	0	2+ 5- 13+ 17+	2+  2 5- -4  0 13+ 17+ -2
Curve Equation t 70720m1 [0,-1,0,-49765,4289637] 2 70720m2 [0,-1,0,-49265,4379537] 2 70720m3 [0,-1,0,-64325,1593125] 2 70720m4 [0,-1,0,248175,12280625] 2
70720n (2 curves)	0	2+ 5- 13+ 17+	2+ -2 5-  0  0 13+ 17+ -2
Curve Equation t 70720n1 [0,1,0,-40,-450] 2 70720n2 [0,1,0,-1145,-15257] 2
70720o (2 curves)	2	2+ 5- 13+ 17+	2+ -2 5-  2 -4 13+ 17+ -4
Curve Equation t Generators 70720o1 [0,1,0,-705,6175] 2 [-30:35:1]&[-7:104:1] 70720o2 [0,1,0,-2785,-50817] 2 [-29:80:1]&[-23:40:1]
70720p (2 curves)	0	2+ 5- 13- 17-	2+  0 5-  2  4 13- 17-  6
Curve Equation t 70720p1 [0,0,0,-1132,6576] 2 70720p2 [0,0,0,3988,49584] 2
70720q (2 curves)	0	2+ 5- 13- 17-	2+  0 5- -2  4 13- 17-  2
Curve Equation t 70720q1 [0,0,0,-920812,-340098384] 2 70720q2 [0,0,0,-920492,-340346576] 2
70720r (2 curves)	0	2+ 5- 13- 17-	2+  2 5-  0 -2 13- 17-  2
Curve Equation t 70720r1 [0,-1,0,-19585,611457] 2 70720r2 [0,-1,0,62335,4330625] 2
70720s (2 curves)	2	2+ 5- 13- 17-	2+ -2 5- -2 -2 13- 17-  0
Curve Equation t Generators 70720s1 [0,1,0,-13265,573775] 2 [-110:845:1]&[-45:1040:1] 70720s2 [0,1,0,255,1701343] 2 [51:-1360:1]&[-19:1300:1]
70720t (2 curves)	2	2- 5+ 13+ 17+	2-  0 5+ -4 -2 13+ 17+ -4
Curve Equation t Generators 70720t1 [0,0,0,-428,848] 2 [-16:60:1]&[-14:64:1] 70720t2 [0,0,0,1652,6672] 2 [12:168:1]&[21:225:1]
70720u (2 curves)	0	2- 5+ 13+ 17+	2-  2 5+  2  0 13+ 17+  4
Curve Equation t 70720u1 [0,-1,0,-601,-5415] 2 70720u2 [0,-1,0,-1121,5921] 2
70720v (2 curves)	0	2- 5+ 13+ 17+	2-  2 5+  2 -4 13+ 17+ -4
Curve Equation t 70720v1 [0,-1,0,-142561,20488065] 2 70720v2 [0,-1,0,-2272481,1319313281] 2
70720w (2 curves)	2	2- 5+ 13+ 17+	2- -2 5+ -2  0 13+ 17+ -4
Curve Equation t Generators 70720w1 [0,1,0,-601,5415] 2 [17:-20:1]&[-11:104:1] 70720w2 [0,1,0,-1121,-5921] 2 [-15:88:1]&[-14:85:1]
70720x (4 curves)	0	2- 5+ 13+ 17+	2- -2 5+ -2  0 13+ 17+ -4
Curve Equation t 70720x1 [0,1,0,-354721,-81434145] 2 70720x2 [0,1,0,-363041,-77422241] 2 70720x3 [0,1,0,-538721,11591455] 2 70720x4 [0,1,0,-6163041,5873257759] 2
70720y (2 curves)	2	2- 5+ 13+ 17+	2- -2 5+ -4  0 13+ 17+  2
Curve Equation t Generators 70720y1 [0,1,0,-261,1435] 2 [-18:25:1]&[-9:56:1] 70720y2 [0,1,0,239,6735] 2 [11:-104:1]&[-13:40:1]
70720z (4 curves)	1	2- 5+ 13+ 17-	2-  0 5+  0  4 13+ 17-  0
Curve Equation t Generators 70720z1 [0,0,0,-2183,53368] 2 [12:170:1] 70720z2 [0,0,0,-38308,2885568] 4 [274:3600:1] 70720z3 [0,0,0,-41708,2342928] 2 [2226:28035:8] 70720z4 [0,0,0,-612908,184689008] 2 [62980:243144:125]
70720ba (4 curves)	1	2- 5+ 13+ 17-	2-  0 5+  0 -4 13+ 17-  0
Curve Equation t Generators 70720ba1 [0,0,0,-2183,-53368] 2 [124:1258:1] 70720ba2 [0,0,0,-38308,-2885568] 4 [27266:4502160:1] 70720ba3 [0,0,0,-41708,-2342928] 2 [1354338:4103189:5832] 70720ba4 [0,0,0,-612908,-184689008] 2 [218162:36011619:8]
70720bb (2 curves)	1	2- 5+ 13+ 17-	2-  0 5+  2  0 13+ 17-  2
Curve Equation t Generators 70720bb1 [0,0,0,-1468,-21648] 2 [5316:41943:64] 70720bb2 [0,0,0,-1388,-24112] 2 [316:5576:1]
70720bc (4 curves)	1	2- 5+ 13+ 17-	2-  0 5+  4  0 13+ 17- -4
Curve Equation t Generators 70720bc1 [0,0,0,-101228,-12280752] 2 [-63868:114920:343] 70720bc2 [0,0,0,-183148,10427472] 4 [-978643986:-54256384000:10503459] 70720bc3 [0,0,0,682132,80688208] 2 [2757:151385:1] 70720bc4 [0,0,0,-2359148,1393493072] 2 [-7458:1214720:27]
70720bd (2 curves)	1	2- 5+ 13+ 17-	2-  2 5+  4  2 13+ 17- -2
Curve Equation t Generators 70720bd1 [0,-1,0,-25041,-1516879] 2 [259167204:19306296415:46656] 70720bd2 [0,-1,0,-24961,-1527135] 2 [22215:3310920:1]
70720be (2 curves)	1	2- 5+ 13- 17+	2-  0 5+  0 -6 13- 17+  0
Curve Equation t Generators 70720be1 [0,0,0,-11948,427728] 2 [29:325:1] 70720be2 [0,0,0,21332,2384592] 2 [-16:1428:1]
70720bf (2 curves)	1	2- 5+ 13- 17+	2- -2 5+  2  0 13- 17+  4
Curve Equation t Generators 70720bf1 [0,1,0,-23041,-842241] 2 [-111:600:1] 70720bf2 [0,1,0,-156161,23092735] 2 [2362:13413:8]
70720bg (2 curves)	0	2- 5+ 13- 17-	2-  2 5+  2  6 13- 17-  4
Curve Equation t 70720bg1 [0,-1,0,84,-2134] 2 70720bg2 [0,-1,0,-2041,-33159] 2
70720bh (2 curves)	2	2- 5+ 13- 17-	2- -2 5+ -2 -6 13- 17- -4
Curve Equation t Generators 70720bh1 [0,1,0,84,2134] 2 [5:52:1]&[57:442:1] 70720bh2 [0,1,0,-2041,33159] 2 [47:-208:1]&[-31:260:1]
70720bi (2 curves)	1	2- 5- 13+ 17+	2-  2 5- -2  4 13+ 17+  4
Curve Equation t Generators 70720bi1 [0,-1,0,-705,-6175] 2 [215:3120:1] 70720bi2 [0,-1,0,-2785,50817] 2 [-51:240:1]
70720bj (4 curves)	1	2- 5- 13+ 17+	2- -2 5-  4  0 13+ 17+  2
Curve Equation t Generators 70720bj1 [0,1,0,-49765,-4289637] 2 [40055:446684:125] 70720bj2 [0,1,0,-49265,-4379537] 2 [1107:36040:1] 70720bj3 [0,1,0,-64325,-1593125] 2 [-50:1225:1] 70720bj4 [0,1,0,248175,-12280625] 2 [75:2600:1]
70720bk (2 curves)	1	2- 5- 13- 17-	2-  0 5-  2 -4 13- 17- -2
Curve Equation t Generators 70720bk1 [0,0,0,-920812,340098384] 2 [298:9600:1] 70720bk2 [0,0,0,-920492,340346576] 2 [517:1625:1]
70720bl (2 curves)	1	2- 5- 13- 17-	2-  0 5- -2 -4 13- 17- -6
Curve Equation t Generators 70720bl1 [0,0,0,-1132,-6576] 2 [290:39:8] 70720bl2 [0,0,0,3988,-49584] 2 [77:845:1]
70720bm (2 curves)	1	2- 5- 13- 17-	2-  2 5-  2  2 13- 17-  0
Curve Equation t Generators 70720bm1 [0,-1,0,-13265,-573775] 2 [175:1560:1] 70720bm2 [0,-1,0,255,-1701343] 2 [8602:281775:8]
70720bn (2 curves)	1	2- 5- 13- 17-	2-  2 5-  2 -2 13- 17-  8
Curve Equation t Generators 70720bn1 [0,-1,0,-23940,-1418038] 2 [208817:4961970:343] 70720bn2 [0,-1,0,-383065,-91127463] 2 [1552111974:17686390735:2000376]
70720bo (2 curves)	1	2- 5- 13- 17-	2- -2 5-  0  2 13- 17- -2
Curve Equation t Generators 70720bo1 [0,1,0,-19585,-611457] 2 [2474:38369:8] 70720bo2 [0,1,0,62335,-4330625] 2 [133:2516:1]
70720bp (2 curves)	1	2- 5- 13- 17-	2- -2 5- -2  2 13- 17- -8
Curve Equation t Generators 70720bp1 [0,1,0,-23940,1418038] 2 [81:130:1] 70720bp2 [0,1,0,-383065,91127463] 2 [2858:-65:8]

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