Cremona's table of elliptic curves

42210 = 2 · 3² · 5 · 7 · 67

Class	r	Atkin-Lehner	Eigenvalues
42210a (2 curves)	2	2+ 3+ 5+ 7- 67+	2+ 3+ 5+ 7- -4 -4 -2  4
Curve Equation t Generators 42210a1 [1,-1,0,-225,1325] 2 [5:15:1]&[-10:55:1] 42210a2 [1,-1,0,-525,-2695] 2 [-14:49:1]&[-13:49:1]
42210b (2 curves)	1	2+ 3+ 5+ 7- 67-	2+ 3+ 5+ 7- -4  4  6 -4
Curve Equation t Generators 42210b1 [1,-1,0,-525,-539] 2 [-7:56:1] 42210b2 [1,-1,0,-5325,150181] 2 [50:59:1]
42210c (2 curves)	2	2+ 3+ 5- 7- 67-	2+ 3+ 5- 7- -4 -2 -8 -4
Curve Equation t Generators 42210c1 [1,-1,0,-7554,-30140] 2 [-84:122:1]&[-79:302:1] 42210c2 [1,-1,0,29946,-262640] 2 [266:-5278:1]&[14:392:1]
42210d (4 curves)	0	2+ 3- 5+ 7+ 67+	2+ 3- 5+ 7+  0  6 -6  4
Curve Equation t 42210d1 [1,-1,0,1350,-94284] 2 42210d2 [1,-1,0,-24570,-1385100] 4 42210d3 [1,-1,0,-77490,6648156] 2 42210d4 [1,-1,0,-386370,-92341620] 2
42210e (2 curves)	1	2+ 3- 5+ 7+ 67-	2+ 3- 5+ 7+  4  4  8  0
Curve Equation t Generators 42210e1 [1,-1,0,-16380,-802224] 2 [-75:51:1] 42210e2 [1,-1,0,-12780,-1167264] 2 [165:1011:1]
42210f (4 curves)	1	2+ 3- 5+ 7+ 67-	2+ 3- 5+ 7+ -4 -2  6 -4
Curve Equation t Generators 42210f1 [1,-1,0,-860280,-308843200] 2 [4355:278050:1] 42210f2 [1,-1,0,-13788600,-19703908864] 4 [-29268513361:14370032633:13651919] 42210f3 [1,-1,0,-13812720,-19631495800] 2 [686278925045:-28761871757835:133432831] 42210f4 [1,-1,0,-220617600,-1261215664264] 2 [-45541682677872337:22770832164841361:5310828573623]
42210g (2 curves)	1	2+ 3- 5+ 7- 67+	2+ 3- 5+ 7-  0  2  0  0
Curve Equation t Generators 42210g1 [1,-1,0,-105,1421] 2 [7:-35:1] 42210g2 [1,-1,0,-2625,52325] 2 [-55:195:1]
42210h (6 curves)	1	2+ 3- 5+ 7- 67+	2+ 3- 5+ 7- -4  6 -2 -4
Curve Equation t Generators 42210h1 [1,-1,0,-58455,-4741475] 2 [-97:143:1] 42210h2 [1,-1,0,-242775,41301661] 4 [-37:7106:1] 42210h3 [1,-1,0,336105,207903325] 2 [-154:12425:1] 42210h4 [1,-1,0,-3770775,2819248861] 4 [998:6521:1] 42210h5 [1,-1,0,-3657375,2996674501] 2 [1187:17483:1] 42210h6 [1,-1,0,-60332175,180388108021] 2 [121215:-75317:27]
42210i (2 curves)	0	2+ 3- 5+ 7- 67-	2+ 3- 5+ 7-  2 -2  0 -4
Curve Equation t 42210i1 [1,-1,0,-1516590,-781800044] 2 42210i2 [1,-1,0,-24854310,-47685949700] 2
42210j (2 curves)	0	2+ 3- 5+ 7- 67-	2+ 3- 5+ 7-  2 -2 -2 -4
Curve Equation t 42210j1 [1,-1,0,23130,-2900300] 2 42210j2 [1,-1,0,-218790,-33914444] 2
42210k (2 curves)	1	2+ 3- 5- 7+ 67+	2+ 3- 5- 7+  2 -2 -2  0
Curve Equation t Generators 42210k1 [1,-1,0,-189,-2187] 2 [39:201:1] 42210k2 [1,-1,0,-3969,-95175] 2 [-36:27:1]
42210l (2 curves)	1	2+ 3- 5- 7+ 67+	2+ 3- 5- 7+  4 -2  0  4
Curve Equation t Generators 42210l1 [1,-1,0,20736,-3490452] 2 [162:1944:1] 42210l2 [1,-1,0,-257094,-45331650] 2 [-299:2327:1]
42210m (2 curves)	0	2+ 3- 5- 7+ 67-	2+ 3- 5- 7+  0  2  2  4
Curve Equation t 42210m1 [1,-1,0,1206,0] 2 42210m2 [1,-1,0,-4824,3618] 2
42210n (2 curves)	0	2- 3+ 5+ 7- 67-	2- 3+ 5+ 7-  4 -2  8 -4
Curve Equation t 42210n1 [1,-1,1,-67988,881767] 2 42210n2 [1,-1,1,269512,6821767] 2
42210o (2 curves)	0	2- 3+ 5- 7- 67+	2- 3+ 5- 7-  4 -4  2  4
Curve Equation t 42210o1 [1,-1,1,-2027,-33749] 2 42210o2 [1,-1,1,-4727,77491] 2
42210p (2 curves)	1	2- 3+ 5- 7- 67-	2- 3+ 5- 7-  4  4 -6 -4
Curve Equation t Generators 42210p1 [1,-1,1,-4727,19279] 2 [-41:398:1] 42210p2 [1,-1,1,-47927,-4006961] 2 [-121:158:1]
42210q (2 curves)	1	2- 3- 5+ 7+ 67+	2- 3- 5+ 7+  0  0  0 -4
Curve Equation t Generators 42210q1 [1,-1,1,-90248,10457547] 2 [165:113:1] 42210q2 [1,-1,1,-86648,11327307] 2 [107:-1863:1]
42210r (4 curves)	0	2- 3- 5+ 7- 67+	2- 3- 5+ 7- -4 -6 -2 -8
Curve Equation t 42210r1 [1,-1,1,-12551014193,-590201275663519] 2 42210r2 [1,-1,1,-205824542513,-35940934627738783] 4 42210r3 [1,-1,1,-210840995633,-34096900506895519] 2 42210r4 [1,-1,1,-3293184542513,-2300234222563738783] 2
42210s (4 curves)	1	2- 3- 5+ 7- 67-	2- 3- 5+ 7-  0  2  0 -4
Curve Equation t Generators 42210s1 [1,-1,1,-29048,-2251753] 2 [82086132:842914313:314432] 42210s2 [1,-1,1,-488318,-131214769] 2 [856185870045180:-33321504551511997:478211768000] 42210s3 [1,-1,1,207877,14675627] 6 [2031:92854:1] 42210s4 [1,-1,1,-903443,122695931] 6 [76403253:9471746906:4913]
42210t (4 curves)	1	2- 3- 5+ 7- 67-	2- 3- 5+ 7-  0 -2 -6  0
Curve Equation t Generators 42210t1 [1,-1,1,-295538,-152719] 2 [-287:7951:1] 42210t2 [1,-1,1,-3244658,2243537777] 4 [-1007:67503:1] 42210t3 [1,-1,1,-1804658,4244561777] 2 [477:-59333:1] 42210t4 [1,-1,1,-51870578,143803316081] 2 [4161:-1793:1]
42210u (4 curves)	1	2- 3- 5+ 7- 67-	2- 3- 5+ 7-  0  6 -6  0
Curve Equation t Generators 42210u1 [1,-1,1,-35663,-2583273] 2 [-55608:28833:512] 42210u2 [1,-1,1,-36383,-2472969] 4 [-930:3811:8] 42210u3 [1,-1,1,36517,-11191809] 2 [1427:53556:1] 42210u4 [1,-1,1,-120803,13296687] 2 [7134:194679:8]
42210v (2 curves)	1	2- 3- 5+ 7- 67-	2- 3- 5+ 7- -4 -2 -6 -4
Curve Equation t Generators 42210v1 [1,-1,1,-788,47031] 2 [-25:237:1] 42210v2 [1,-1,1,-24908,1513527] 2 [71:279:1]
42210w (2 curves)	1	2- 3- 5- 7- 67+	2- 3- 5- 7-  2 -6  4  4
Curve Equation t Generators 42210w1 [1,-1,1,-12542,780941] 2 [201:-2621:1] 42210w2 [1,-1,1,-224222,40915469] 2 [327:-1739:1]
42210x (4 curves)	0	2- 3- 5- 7- 67-	2- 3- 5- 7-  0  2 -2 -4
Curve Equation t 42210x1 [1,-1,1,-452,3799] 2 42210x2 [1,-1,1,-632,631] 4 42210x3 [1,-1,1,2518,3151] 2 42210x4 [1,-1,1,-6662,-206801] 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