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	4	Product of Tamagawa factors cp
Δ	11967264 = 25 · 39 · 19	Discriminant
Eigenvalues	2+ 3- -2  0  4  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-787968,269419360]	[a1,a2,a3,a4,a6]
j	74220219816682217473/16416	j-invariant
L	0.91932346865948	L(r)(E,1)/r!
Ω	0.91932346865948	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	2736v3 10944bg3 114c3 8550w3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342f3

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 342f3

-4	8	-3	5	-7	-11	13	17	-19
2736v3	10944bg3	114c3	8550w3	16758n3	41382cm4	57798bm4	98838i4	6498w3

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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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