Cremona's table of elliptic curves

342 = 2 · 3² · 19

Class	r	Atkin-Lehner	Eigenvalues
342e (2 curves)	1	2+ 3+ 19+	2+ 3+ -2  0 -2 -4  0 19+
Curve Equation t Generators 342e1 [1,-1,0,-3,1] 2 [-1:2:1] 342e2 [1,-1,0,-33,-65] 2 [-3:2:1]
342f (4 curves)	0	2+ 3- 19+	2+ 3- -2  0  4  2  6 19+
Curve Equation t 342f1 [1,-1,0,-3168,62464] 2 342f2 [1,-1,0,-49248,4218880] 4 342f3 [1,-1,0,-787968,269419360] 2 342f4 [1,-1,0,-47808,4476064] 2
342g (2 curves)	0	2+ 3- 19+	2+ 3-  4  3 -2 -1 -3 19+
Curve Equation t 342g1 [1,-1,0,0,-32] 1 342g2 [1,-1,0,-630,6898] 1
342c (4 curves)	1	2+ 3- 19-	2+ 3-  0 -4  0 -4 -6 19-
Curve Equation t Generators 342c1 [1,-1,0,-72,0] 2 [-3:15:1] 342c2 [1,-1,0,288,-216] 2 [15:78:1] 342c3 [1,-1,0,-3852,92988] 6 [-39:447:1] 342c4 [1,-1,0,-3762,97470] 6 [39:75:1]
342d (2 curves)	0	2- 3+ 19+	2- 3+  2  0  2 -4  0 19+
Curve Equation t 342d1 [1,-1,1,-29,1] 2 342d2 [1,-1,1,-299,2053] 2
342a (3 curves)	0	2- 3- 19-	2- 3-  0 -1  6  5 -3 19-
Curve Equation t 342a1 [1,-1,1,-140,-601] 1 342a2 [1,-1,1,85,-2437] 3 342a3 [1,-1,1,-770,66305] 3
342b (2 curves)	0	2- 3- 19-	2- 3-  0  4 -4  0  2 19-
Curve Equation t 342b1 [1,-1,1,-860,9915] 2 342b2 [1,-1,1,-770,12003] 2

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

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