Cremona's table of elliptic curves

84870 = 2 · 3² · 5 · 23 · 41

Class	r	Atkin-Lehner	Eigenvalues
84870a (2 curves)	1	2+ 3- 5+ 23+ 41-	2+ 3- 5+  0 -2  4  0  2
Curve Equation t Generators 84870a1 [1,-1,0,-330,1376] 2 [-7:61:1] 84870a2 [1,-1,0,-2400,-43750] 2 [-25:25:1]
84870b (1 curve)	1	2+ 3- 5+ 23+ 41-	2+ 3- 5+  1  2 -6  5  8
Curve Equation t Generators 84870b1 [1,-1,0,360,-4374] 1 [81:702:1]
84870c (2 curves)	1	2+ 3- 5+ 23+ 41-	2+ 3- 5+ -4  2  4  0 -2
Curve Equation t Generators 84870c1 [1,-1,0,-18773460,13585006800] 2 [31371015:-3674429195:59319] 84870c2 [1,-1,0,-154432980,-729313656624] 2 [-47022911911159041:554141532795962333:6277363000623]
84870d (2 curves)	1	2+ 3- 5+ 23+ 41-	2+ 3- 5+ -4 -2  0  8 -2
Curve Equation t Generators 84870d1 [1,-1,0,-45450,3712500] 2 [-75:2625:1] 84870d2 [1,-1,0,-78570,-2388204] 2 [-107:2241:1]
84870e (1 curve)	1	2+ 3- 5+ 23- 41+	2+ 3- 5+  1  4 -4 -5 -8
Curve Equation t Generators 84870e1 [1,-1,0,4635,-34155] 1 [174:2127:8]
84870f (4 curves)	1	2+ 3- 5+ 23- 41+	2+ 3- 5+  4  0  6 -6  0
Curve Equation t Generators 84870f1 [1,-1,0,-36900,-2718464] 2 [1652:65828:1] 84870f2 [1,-1,0,-41400,-2010164] 4 [-57:431:1] 84870f3 [1,-1,0,124650,-14198234] 2 [6585:531791:1] 84870f4 [1,-1,0,-279450,55455106] 2 [357:868:1]
84870g (1 curve)	0	2+ 3- 5+ 23- 41-	2+ 3- 5+ -1  4  4  7  0
Curve Equation t 84870g1 [1,-1,0,-1395,266575] 1
84870h (4 curves)	0	2+ 3- 5+ 23- 41-	2+ 3- 5+  2  0 -4  0 -4
Curve Equation t 84870h1 [1,-1,0,-119565,-15882075] 2 84870h2 [1,-1,0,-111285,-18182259] 2 84870h3 [1,-1,0,-250065,24453225] 6 84870h4 [1,-1,0,844965,180166491] 6
84870i (2 curves)	1	2+ 3- 5- 23+ 41+	2+ 3- 5- -2  2 -6  4 -6
Curve Equation t Generators 84870i1 [1,-1,0,-4179024,-2981016320] 2 [-4616928:-50518928:4913] 84870i2 [1,-1,0,-65119824,-202245244160] 2 [-1820465017551:1480812716329:390617891]
84870j (2 curves)	1	2+ 3- 5- 23+ 41+	2+ 3- 5- -2  6  6  0  6
Curve Equation t Generators 84870j1 [1,-1,0,-517419,136851525] 2 [94:9389:1] 84870j2 [1,-1,0,-1469619,-510454035] 2 [-134393:841791:343]
84870k (1 curve)	1	2+ 3- 5- 23+ 41+	2+ 3- 5- -5  0  0  3  0
Curve Equation t Generators 84870k1 [1,-1,0,621,-9315] 1 [21:102:1]
84870l (2 curves)	0	2+ 3- 5- 23+ 41-	2+ 3- 5-  0  0  6  4 -6
Curve Equation t 84870l1 [1,-1,0,486,-17420] 2 84870l2 [1,-1,0,-7794,-244292] 2
84870m (2 curves)	0	2+ 3- 5- 23+ 41-	2+ 3- 5-  0  2  4 -2  0
Curve Equation t 84870m1 [1,-1,0,-136584,21757248] 2 84870m2 [1,-1,0,-2256264,1305011520] 2
84870n (2 curves)	0	2+ 3- 5- 23+ 41-	2+ 3- 5-  0  2  4  4  6
Curve Equation t 84870n1 [1,-1,0,-15611499,17074508805] 2 84870n2 [1,-1,0,40638501,112013258805] 2
84870o (2 curves)	0	2+ 3- 5- 23+ 41-	2+ 3- 5- -2  0 -4 -6  0
Curve Equation t 84870o1 [1,-1,0,-35781939,78879785845] 2 84870o2 [1,-1,0,-565701939,5178935849845] 2
84870p (2 curves)	0	2+ 3- 5- 23- 41+	2+ 3- 5-  2  6  2  0 -2
Curve Equation t 84870p1 [1,-1,0,-21474,-230432] 2 84870p2 [1,-1,0,-259524,-50744642] 2
84870q (1 curve)	0	2+ 3- 5- 23- 41+	2+ 3- 5- -3 -6  6  1  0
Curve Equation t 84870q1 [1,-1,0,-666594,-209802092] 1
84870r (2 curves)	1	2+ 3- 5- 23- 41-	2+ 3- 5-  0 -2 -4  4 -2
Curve Equation t Generators 84870r1 [1,-1,0,-509139,-134666955] 2 [-359:1502:1] 84870r2 [1,-1,0,-1337139,415290645] 2 [1081:14697:1]
84870s (2 curves)	1	2+ 3- 5- 23- 41-	2+ 3- 5-  0 -6  0 -8 -6
Curve Equation t Generators 84870s1 [1,-1,0,-119754,-15877472] 2 [-198:304:1] 84870s2 [1,-1,0,-171504,-776822] 2 [837:20594:1]
84870t (2 curves)	1	2+ 3- 5- 23- 41-	2+ 3- 5-  4  2 -4  0  2
Curve Equation t Generators 84870t1 [1,-1,0,-345069,78053733] 2 [322:339:1] 84870t2 [1,-1,0,-5520069,4993268733] 2 [1357:-661:1]
84870u (2 curves)	1	2+ 3- 5- 23- 41-	2+ 3- 5- -4  0 -7  6  5
Curve Equation t Generators 84870u1 [1,-1,0,9621,37125] 1 [40806:610381:729] 84870u2 [1,-1,0,-140139,21319173] 3 [-218:6549:1]
84870v (2 curves)	1	2+ 3- 5- 23- 41-	2+ 3- 5- -4  6  0  0  2
Curve Equation t Generators 84870v1 [1,-1,0,-24399,-962195] 2 [-49:362:1] 84870v2 [1,-1,0,-156879,23228653] 2 [-43:5489:1]
84870w (2 curves)	1	2- 3- 5+ 23+ 41+	2- 3- 5+ -2  2  6 -4 -6
Curve Equation t Generators 84870w1 [1,-1,1,-43538,-3123583] 2 [-105:583:1] 84870w2 [1,-1,1,59962,-15791983] 2 [1045:33933:1]
84870x (2 curves)	1	2- 3- 5+ 23+ 41+	2- 3- 5+  4  0 -2  2  6
Curve Equation t Generators 84870x1 [1,-1,1,1957,18407] 2 [414:3839:8] 84870x2 [1,-1,1,-9113,164531] 2 [-6252:24829:64]
84870y (1 curve)	1	2- 3- 5+ 23+ 41+	2- 3- 5+ -5  6 -2 -7  0
Curve Equation t Generators 84870y1 [1,-1,1,-12704558,-28734116803] 1 [7641:562099:1]
84870z (1 curve)	0	2- 3- 5+ 23- 41+	2- 3- 5+  1  4  4  7  8
Curve Equation t 84870z1 [1,-1,1,-236048,-44082669] 1
84870ba (2 curves)	0	2- 3- 5+ 23- 41+	2- 3- 5+  2 -2 -2  4  2
Curve Equation t 84870ba1 [1,-1,1,-1733,-231123] 2 84870ba2 [1,-1,1,-68153,-6793419] 2
84870bb (4 curves)	0	2- 3- 5+ 23- 41+	2- 3- 5+  2  6  2  6  2
Curve Equation t 84870bb1 [1,-1,1,-30173,-465919] 2 84870bb2 [1,-1,1,-288923,59460581] 2 84870bb3 [1,-1,1,-1460048,679398131] 6 84870bb4 [1,-1,1,-23360648,43464410291] 6
84870bc (2 curves)	2	2- 3- 5+ 23- 41+	2- 3- 5+ -2 -6 -2  4 -6
Curve Equation t Generators 84870bc1 [1,-1,1,922012,495537031] 2 [-425:5387:1]&[541:-34219:1] 84870bc2 [1,-1,1,-6635108,5186997127] 2 [-2707:58853:1]&[-2155:98413:1]
84870bd (2 curves)	0	2- 3- 5+ 23- 41+	2- 3- 5+  4  4 -2  0 -4
Curve Equation t 84870bd1 [1,-1,1,-40523,-108453] 2 84870bd2 [1,-1,1,-454523,-117518853] 2
84870be (2 curves)	1	2- 3- 5+ 23- 41-	2- 3- 5+  2  0 -4  6  0
Curve Equation t Generators 84870be1 [1,-1,1,-2003,2531] 2 [1:22:1] 84870be2 [1,-1,1,-22703,1319051] 2 [91:-24:1]
84870bf (2 curves)	1	2- 3- 5- 23+ 41-	2- 3- 5-  0  6  0 -2 -6
Curve Equation t Generators 84870bf1 [1,-1,1,-42467,2323491] 2 [-49:2094:1] 84870bf2 [1,-1,1,-618467,187334691] 2 [551:-3966:1]
84870bg (2 curves)	1	2- 3- 5- 23- 41+	2- 3- 5-  2 -6 -2  4 -2
Curve Equation t Generators 84870bg1 [1,-1,1,-1431977,-663390871] 2 [2367:94756:1] 84870bg2 [1,-1,1,-22952057,-42317657719] 2 [6741:327154:1]
84870bh (2 curves)	1	2- 3- 5- 23- 41+	2- 3- 5- -4  0 -2  4  4
Curve Equation t Generators 84870bh1 [1,-1,1,-3587,77699] 2 [7:226:1] 84870bh2 [1,-1,1,3613,345539] 2 [39:-758:1]
84870bi (1 curve)	0	2- 3- 5- 23- 41-	2- 3- 5-  0  0  5  2  5
Curve Equation t 84870bi1 [1,-1,1,-32,371] 1
84870bj (2 curves)	0	2- 3- 5- 23- 41-	2- 3- 5-  4  2 -4  0  2
Curve Equation t 84870bj1 [1,-1,1,-22749377,36497976401] 2 84870bj2 [1,-1,1,36233023,194264099921] 2

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