Cremona's table of elliptic curves

42570 = 2 · 3² · 5 · 11 · 43

Class	r	Atkin-Lehner	Eigenvalues
42570a (2 curves)	2	2+ 3+ 5+ 11+ 43-	2+ 3+ 5+ -2 11+ -6 -6  2
Curve Equation t Generators 42570a1 [1,-1,0,-315,2225] 2 [16:-41:1]&[-17:58:1] 42570a2 [1,-1,0,-165,4235] 2 [11:-66:1]&[46:447:8]
42570b (4 curves)	1	2+ 3+ 5+ 11- 43-	2+ 3+ 5+  2 11-  2 -6  2
Curve Equation t Generators 42570b1 [1,-1,0,-4761030,3999712500] 6 [29316:-297122:27] 42570b2 [1,-1,0,-4760430,4000770540] 6 [80494134:-818392513:74088] 42570b3 [1,-1,0,-4835445,3868282421] 2 [-1030:88579:1] 42570b4 [1,-1,0,3804555,16176826421] 2 [-1490:995507:8]
42570c (2 curves)	0	2+ 3- 5+ 11+ 43+	2+ 3- 5+  0 11+  6 -2  2
Curve Equation t 42570c1 [1,-1,0,70177320,-206585412800] 2 42570c2 [1,-1,0,-387783000,-1919448601664] 2
42570d (1 curve)	0	2+ 3- 5+ 11+ 43+	2+ 3- 5+ -1 11+ -5  2  1
Curve Equation t 42570d1 [1,-1,0,130365,-26412075] 1
42570e (1 curve)	0	2+ 3- 5+ 11+ 43+	2+ 3- 5+  3 11+  3 -2 -7
Curve Equation t 42570e1 [1,-1,0,-12780,-650714] 1
42570f (1 curve)	0	2+ 3- 5+ 11+ 43+	2+ 3- 5+  5 11+  4 -1  7
Curve Equation t 42570f1 [1,-1,0,-2970,64746] 1
42570g (2 curves)	1	2+ 3- 5+ 11+ 43-	2+ 3- 5+  1 11+  0  3 -1
Curve Equation t Generators 42570g1 [1,-1,0,-50240355,-137054845675] 1 [6473857997723546251646834345976478100489187741:-2136830784275131678338915695551104328723889868799:59344383730316389990785863019538164499887] 42570g2 [1,-1,0,361297695,2593739367395] 1 [-5071838013:-725102484893:970299]
42570h (1 curve)	1	2+ 3- 5+ 11+ 43-	2+ 3- 5+ -3 11+ -4  3  3
Curve Equation t Generators 42570h1 [1,-1,0,315,9045] 1 [7:104:1]
42570i (1 curve)	1	2+ 3- 5+ 11- 43+	2+ 3- 5+ -1 11-  3 -4 -1
Curve Equation t Generators 42570i1 [1,-1,0,-2074545,1150611075] 1 [831:-465:1]
42570j (4 curves)	0	2+ 3- 5+ 11- 43-	2+ 3- 5+  0 11- -2 -2  8
Curve Equation t 42570j1 [1,-1,0,-21930,-1294300] 2 42570j2 [1,-1,0,-354750,-81237664] 4 42570j3 [1,-1,0,-358620,-79371550] 2 42570j4 [1,-1,0,-5676000,-5203472914] 2
42570k (6 curves)	0	2+ 3- 5+ 11- 43-	2+ 3- 5+  0 11-  6 -2  4
Curve Equation t 42570k1 [1,-1,0,-298305,-62290499] 2 42570k2 [1,-1,0,-482625,24008125] 4 42570k3 [1,-1,0,1893375,188902525] 2 42570k4 [1,-1,0,-5807745,5380013821] 4 42570k5 [1,-1,0,-3934665,8908521925] 2 42570k6 [1,-1,0,-92882745,344571968821] 2
42570l (4 curves)	0	2+ 3- 5+ 11- 43-	2+ 3- 5+ -4 11-  2  6 -4
Curve Equation t 42570l1 [1,-1,0,-6120,-290304] 2 42570l2 [1,-1,0,-113040,-14596200] 2 42570l3 [1,-1,0,50580,4846716] 6 42570l4 [1,-1,0,-308790,47324250] 6
42570m (1 curve)	1	2+ 3- 5- 11+ 43+	2+ 3- 5- -2 11+  4  0 -2
Curve Equation t Generators 42570m1 [1,-1,0,-54,-572] 1 [12:14:1]
42570n (2 curves)	1	2+ 3- 5- 11- 43-	2+ 3- 5-  2 11- -4  0  2
Curve Equation t Generators 42570n1 [1,-1,0,-35244,-2602800] 1 [5474088:56470636:19683] 42570n2 [1,-1,0,160596,-10074672] 3 [712:21204:1]
42570o (1 curve)	1	2+ 3- 5- 11- 43-	2+ 3- 5-  3 11-  1  4 -7
Curve Equation t Generators 42570o1 [1,-1,0,-4299,170693] 1 [37:-266:1]
42570p (4 curves)	1	2+ 3- 5- 11- 43-	2+ 3- 5- -4 11-  2 -2  4
Curve Equation t Generators 42570p1 [1,-1,0,8901,90085] 2 [159:2267:1] 42570p2 [1,-1,0,-37179,762853] 4 [-106:1925:1] 42570p3 [1,-1,0,-346779,-77937467] 2 [-321:635:1] 42570p4 [1,-1,0,-464859,121967365] 2 [-79:12617:1]
42570q (4 curves)	0	2- 3+ 5- 11+ 43-	2- 3+ 5-  2 11+  2  6  2
Curve Equation t 42570q1 [1,-1,1,-537272,-143090629] 6 42570q2 [1,-1,1,422728,-599282629] 6 42570q3 [1,-1,1,-42849272,-107949388229] 2 42570q4 [1,-1,1,-42843872,-107977960709] 2
42570r (2 curves)	1	2- 3+ 5- 11- 43-	2- 3+ 5- -2 11- -6  6  2
Curve Equation t Generators 42570r1 [1,-1,1,-2837,-57239] 2 [2198:34537:8] 42570r2 [1,-1,1,-1487,-112859] 2 [59154:935411:216]
42570s (2 curves)	0	2- 3- 5+ 11+ 43-	2- 3- 5+  0 11+  2  6  0
Curve Equation t 42570s1 [1,-1,1,18067,632981] 2 42570s2 [1,-1,1,-88853,5636837] 2
42570t (2 curves)	0	2- 3- 5+ 11+ 43-	2- 3- 5+  0 11+  2 -6  6
Curve Equation t 42570t1 [1,-1,1,-66038,-6518779] 2 42570t2 [1,-1,1,-1056758,-417865723] 2
42570u (1 curve)	0	2- 3- 5+ 11+ 43-	2- 3- 5+  5 11+  5 -4 -5
Curve Equation t 42570u1 [1,-1,1,-1259978,-815987703] 1
42570v (4 curves)	0	2- 3- 5+ 11- 43+	2- 3- 5+  0 11-  2 -6 -8
Curve Equation t 42570v1 [1,-1,1,-10958,-2389683] 2 42570v2 [1,-1,1,-343778,-77207619] 4 42570v3 [1,-1,1,-517928,9449421] 2 42570v4 [1,-1,1,-5494748,-4956206403] 2
42570w (2 curves)	1	2- 3- 5+ 11- 43-	2- 3- 5+  0 11-  0 -8  4
Curve Equation t Generators 42570w1 [1,-1,1,-10948568,-13941330213] 2 [9965:925833:1] 42570w2 [1,-1,1,-175177688,-892370047269] 2 [15311:113241:1]
42570x (4 curves)	1	2- 3- 5+ 11- 43-	2- 3- 5+  0 11-  6 -2 -4
Curve Equation t Generators 42570x1 [1,-1,1,-269048,53780347] 2 [283:-637:1] 42570x2 [1,-1,1,-280568,48932731] 4 [-395:10097:1] 42570x3 [1,-1,1,493432,270606331] 2 [-137:14225:1] 42570x4 [1,-1,1,-1238888,-483126533] 2 [-637:7193:1]
42570y (1 curve)	1	2- 3- 5+ 11- 43-	2- 3- 5+ -3 11- -3 -2  1
Curve Equation t Generators 42570y1 [1,-1,1,247,897] 1 [17:90:1]
42570z (4 curves)	1	2- 3- 5+ 11- 43-	2- 3- 5+ -4 11- -4  0  8
Curve Equation t Generators 42570z1 [1,-1,1,-12426413,25786575281] 2 [-4029:104182:1] 42570z2 [1,-1,1,-226774283,1314188752277] 2 [1266846:501292415:8] 42570z3 [1,-1,1,-1147971488,14971080405251] 6 [437523282:170827485305:2744] 42570z4 [1,-1,1,-18367544408,958135304037827] 6 [10119546002003451:-4880806198857835:129323920193]
42570ba (2 curves)	1	2- 3- 5- 11+ 43-	2- 3- 5-  0 11+ -4 -8  0
Curve Equation t Generators 42570ba1 [1,-1,1,-92,-881] 2 [19:53:1] 42570ba2 [1,-1,1,-2072,-35729] 2 [85:587:1]
42570bb (4 curves)	1	2- 3- 5- 11+ 43-	2- 3- 5-  0 11+  6 -6  0
Curve Equation t Generators 42570bb1 [1,-1,1,-92417,21597441] 2 [101:-3696:1] 42570bb2 [1,-1,1,-1856597,973548969] 4 [-573:43286:1] 42570bb3 [1,-1,1,-2239727,543064101] 2 [32158:1885167:8] 42570bb4 [1,-1,1,-29700347,62307761469] 2 [39966:1551663:8]
42570bc (2 curves)	1	2- 3- 5- 11+ 43-	2- 3- 5- -2 11+ -2  6  0
Curve Equation t Generators 42570bc1 [1,-1,1,-2327,-27921] 2 [-33:126:1] 42570bc2 [1,-1,1,6673,-197121] 2 [57:576:1]
42570bd (4 curves)	1	2- 3- 5- 11- 43+	2- 3- 5-  0 11- -2 -6  8
Curve Equation t Generators 42570bd1 [1,-1,1,-4127,79751] 4 [-69:214:1] 42570bd2 [1,-1,1,-22127,-1194649] 4 [-99:184:1] 42570bd3 [1,-1,1,16573,-4956289] 2 [159:1216:1] 42570bd4 [1,-1,1,-348827,-79210609] 2 [-341:184:1]
42570be (2 curves)	0	2- 3- 5- 11- 43-	2- 3- 5-  2 11- -2  6  0
Curve Equation t 42570be1 [1,-1,1,-236912,44443311] 2 42570be2 [1,-1,1,-234662,45327111] 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