Cremona's table of elliptic curves

16770 = 2 · 3 · 5 · 13 · 43

Class	r	Atkin-Lehner	Eigenvalues
16770a (2 curves)	0	2+ 3+ 5- 13+ 43+	2+ 3+ 5-  4  0 13+  2  0
Curve Equation t 16770a1 [1,1,0,3898,48324] 2 16770a2 [1,1,0,-17602,388024] 2
16770b (2 curves)	0	2+ 3+ 5- 13+ 43+	2+ 3+ 5-  4 -2 13+  4 -2
Curve Equation t 16770b1 [1,1,0,-3842,44196] 2 16770b2 [1,1,0,13058,345016] 2
16770c (2 curves)	1	2+ 3+ 5- 13+ 43-	2+ 3+ 5- -2  4 13+ -6  8
Curve Equation t Generators 16770c1 [1,1,0,-75075982,240579143476] 2 [12012:1029434:1] 16770c2 [1,1,0,39168018,907969742676] 2 [5877:1155159:1]
16770d (4 curves)	0	2+ 3- 5+ 13+ 43+	2+ 3- 5+  0  0 13+ -6  0
Curve Equation t 16770d1 [1,0,1,-290194,45493412] 2 16770d2 [1,0,1,-1600914,-741987164] 4 16770d3 [1,0,1,-25268114,-48890538844] 2 16770d4 [1,0,1,1094766,-2986949468] 2
16770e (4 curves)	1	2+ 3- 5+ 13- 43+	2+ 3- 5+  0 -4 13-  2 -4
Curve Equation t Generators 16770e1 [1,0,1,71,-244] 2 [4:8:1] 16770e2 [1,0,1,-429,-2444] 4 [-16:27:1] 16770e3 [1,0,1,-6279,-191984] 2 [-46:27:1] 16770e4 [1,0,1,-2579,48296] 2 [-54:202:1]
16770f (4 curves)	1	2+ 3- 5+ 13- 43+	2+ 3- 5+ -4 -4 13-  2  0
Curve Equation t Generators 16770f1 [1,0,1,-6344,-183274] 2 [-42:118:1] 16770f2 [1,0,1,-19864,855062] 4 [-59:1379:1] 16770f3 [1,0,1,-299364,63015862] 2 [-229:11049:1] 16770f4 [1,0,1,43316,5201846] 2 [58:2783:1]
16770g (2 curves)	1	2+ 3- 5- 13+ 43+	2+ 3- 5-  0 -4 13+  4  4
Curve Equation t Generators 16770g1 [1,0,1,-110293,13248608] 2 [-56:4415:1] 16770g2 [1,0,1,-1735293,879698608] 2 [794:1215:1]
16770h (2 curves)	1	2+ 3- 5- 13+ 43+	2+ 3- 5- -2  2 13+  6  2
Curve Equation t Generators 16770h1 [1,0,1,-2393,40556] 2 [-30:307:1] 16770h2 [1,0,1,-8893,-279244] 2 [-50:227:1]
16770i (2 curves)	1	2+ 3- 5- 13+ 43+	2+ 3- 5- -2  4 13+ -4  6
Curve Equation t Generators 16770i1 [1,0,1,-357098,83065628] 2 [309:1345:1] 16770i2 [1,0,1,-5732098,5281765628] 2 [-266:82520:1]
16770j (2 curves)	0	2+ 3- 5- 13+ 43-	2+ 3- 5- -2 -2 13+  0 -6
Curve Equation t 16770j1 [1,0,1,-1050738068,-13109698820194] 2 16770j2 [1,0,1,-1050769318,-13108880045194] 2
16770k (2 curves)	0	2+ 3- 5- 13+ 43-	2+ 3- 5- -2  6 13+  0 -6
Curve Equation t 16770k1 [1,0,1,-508,-4294] 2 16770k2 [1,0,1,-1308,12346] 2
16770l (2 curves)	0	2+ 3- 5- 13+ 43-	2+ 3- 5-  4  4 13+  6  0
Curve Equation t 16770l1 [1,0,1,-2193233,-1445671132] 2 16770l2 [1,0,1,-36593233,-85202791132] 2
16770m (2 curves)	2	2+ 3- 5- 13+ 43-	2+ 3- 5- -4 -6 13+ -6 -2
Curve Equation t Generators 16770m1 [1,0,1,-1743,26158] 2 [-46:120:1]&[-31:240:1] 16770m2 [1,0,1,1507,113258] 2 [-36:130:1]&[-18:292:1]
16770n (2 curves)	0	2- 3+ 5+ 13+ 43+	2- 3+ 5+  2 -6 13+ -2 -6
Curve Equation t 16770n1 [1,1,1,-9215761,-10771756561] 2 16770n2 [1,1,1,-9631761,-9746566161] 2
16770o (2 curves)	0	2- 3+ 5+ 13+ 43+	2- 3+ 5+  4  0 13+  0  4
Curve Equation t 16770o1 [1,1,1,-261,1383] 2 16770o2 [1,1,1,-911,-9277] 2
16770p (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+  2  0 13+ -8  2
Curve Equation t Generators 16770p1 [1,1,1,36354,29662779] 2 [-21:5385:1] 16770p2 [1,1,1,-1243646,514014779] 2 [401:8743:1]
16770q (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+  2  2 13+  0 -6
Curve Equation t Generators 16770q1 [1,1,1,-36271,-2620171] 2 [-119:228:1] 16770q2 [1,1,1,-577071,-168970251] 2 [-439:228:1]
16770r (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+  2  4 13+  4  2
Curve Equation t Generators 16770r1 [1,1,1,-9166,334859] 2 [49:55:1] 16770r2 [1,1,1,-146766,21580299] 2 [133:2039:1]
16770s (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+  2 -6 13+  4  2
Curve Equation t Generators 16770s1 [1,1,1,-2380086,-1414295217] 2 [-25482827181713427:11480158745676801:28632956937857] 16770s2 [1,1,1,-38081336,-90467493217] 2 [-142573956911005641910871263782157666:71268462960128030402918087499127783:40012339170074607209603153014856]
16770t (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+ -2  2 13+  0  2
Curve Equation t Generators 16770t1 [1,1,1,-18196,934193] 2 [73:3:1] 16770t2 [1,1,1,-26646,-32487] 2 [-1106:8679:8]
16770u (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+ -2 -2 13+  4  2
Curve Equation t Generators 16770u1 [1,1,1,-8864436,-8896537611] 2 [-1219:10593:1] 16770u2 [1,1,1,-136864436,-616333337611] 2 [-182913:146875:27]
16770v (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+  4 -2 13+ -2  2
Curve Equation t Generators 16770v1 [1,1,1,-1671,25593] 2 [-9:204:1] 16770v2 [1,1,1,-1541,29909] 2 [654:5087:8]
16770w (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+ -4 -2 13+  2 -6
Curve Equation t Generators 16770w1 [1,1,1,-41256,3123753] 2 [51:1049:1] 16770w2 [1,1,1,10744,10528553] 2 [87:3439:1]
16770x (2 curves)	1	2- 3+ 5+ 13+ 43-	2- 3+ 5+ -4 -2 13+ -2  2
Curve Equation t Generators 16770x1 [1,1,1,-11020291,-14085728287] 2 [13111:1440994:1] 16770x2 [1,1,1,-11018211,-14091308511] 2 [64414207:-7144035810:4913]
16770y (2 curves)	1	2- 3+ 5+ 13- 43+	2- 3+ 5+  2 -2 13- -4 -2
Curve Equation t Generators 16770y1 [1,1,1,-4301,-109501] 2 [-37:44:1] 16770y2 [1,1,1,-7501,70979] 2 [-59:588:1]
16770z (6 curves)	0	2- 3+ 5- 13- 43+	2- 3+ 5-  0  4 13- -6 -4
Curve Equation t 16770z1 [1,1,1,-33200,38417] 4 16770z2 [1,1,1,-360880,-83323375] 8 16770z3 [1,1,1,-5768880,-5335572975] 4 16770z4 [1,1,1,-195760,-159674863] 4 16770z5 [1,1,1,-92302080,-341361295215] 2 16770z6 [1,1,1,-5763680,-5345665135] 2
16770ba (2 curves)	1	2- 3- 5+ 13+ 43+	2- 3- 5+  0  0 13+  0  0
Curve Equation t Generators 16770ba1 [1,0,0,-11311,432185] 2 [86:-355:1] 16770ba2 [1,0,0,-177711,28820025] 2 [246:-51:1]
16770bb (2 curves)	1	2- 3- 5+ 13+ 43+	2- 3- 5+ -2  2 13+ -2 -2
Curve Equation t Generators 16770bb1 [1,0,0,-1736,-27840] 2 [-24:24:1] 16770bb2 [1,0,0,-27736,-1780240] 2 [194:290:1]
16770bc (2 curves)	1	2- 3- 5+ 13+ 43+	2- 3- 5+ -2 -4 13+  4 -2
Curve Equation t Generators 16770bc1 [1,0,0,-98796,34290576] 2 [-264:6612:1] 16770bc2 [1,0,0,-2300396,1340720016] 2 [760:5236:1]
16770bd (2 curves)	1	2- 3- 5+ 13- 43-	2- 3- 5+  0 -6 13- -2 -2
Curve Equation t Generators 16770bd1 [1,0,0,-466,1796] 2 [56:-418:1] 16770bd2 [1,0,0,1614,13860] 2 [24:246:1]
16770be (4 curves)	0	2- 3- 5- 13+ 43+	2- 3- 5-  0 -4 13+ -2  4
Curve Equation t 16770be1 [1,0,0,565,1137] 4 16770be2 [1,0,0,-2315,8625] 4 16770be3 [1,0,0,-22595,-1301463] 2 16770be4 [1,0,0,-28115,1809465] 2
16770bf (4 curves)	1	2- 3- 5- 13- 43+	2- 3- 5-  0  0 13- -6 -4
Curve Equation t Generators 16770bf1 [1,0,0,410,16100] 4 [-10:110:1] 16770bf2 [1,0,0,-7590,238500] 4 [-48:726:1] 16770bf3 [1,0,0,-23790,-1125540] 2 [-78:546:1] 16770bf4 [1,0,0,-119390,15868140] 2 [202:-38:1]
16770bg (4 curves)	0	2- 3- 5- 13- 43-	2- 3- 5- -4  4 13-  6  4
Curve Equation t 16770bg1 [1,0,0,-180,912] 2 16770bg2 [1,0,0,-260,0] 4 16770bg3 [1,0,0,-2840,-58308] 2 16770bg4 [1,0,0,1040,260] 4

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