Cremona's table of elliptic curves

342 = 2 · 3² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3- 19+	Signs for the Atkin-Lehner involutions
Class	342f	Isogeny class
Conductor	342	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1615648817503008 = -1 · 25 · 318 · 194	Discriminant
Eigenvalues	2+ 3- -2  0  4  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-47808,4476064]	[a1,a2,a3,a4,a6]
j	-16576888679672833/2216253521952	j-invariant
L	0.91932346865948	L(r)(E,1)/r!
Ω	0.45966173432974	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2736v4 10944bg4 114c4 8550w4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342f4

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	-2	0	4	2	6	+	4	2	4	10	-10	4	4	10	-12	14	-12	-8	-6	-4	-12	6	10

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Quadratic twists for elliptic curve 342f4

-4	8	-3	5	-7	-11	13	17	-19
2736v4	10944bg4	114c4	8550w4	16758n4	41382cm3	57798bm3	98838i3	6498w4

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

Part of Computational Number Theory
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