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	16	Product of Tamagawa factors cp
Δ	196454605824 = 210 · 312 · 192	Discriminant
Eigenvalues	2+ 3- -2  0  4  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-49248,4218880]	[a1,a2,a3,a4,a6]
j	18120364883707393/269485056	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	4	Number of elements in the torsion subgroup
Twists	2736v2 10944bg2 114c2 8550w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 342f2

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 342f2

-4	8	-3	5	-7	-11	13	17	-19
2736v2	10944bg2	114c2	8550w2	16758n2	41382cm2	57798bm2	98838i2	6498w2

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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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