Cremona's table of elliptic curves

3486 = 2 · 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 83+	Signs for the Atkin-Lehner involutions
Class	3486j	Isogeny class
Conductor	3486	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	562473072 = 24 · 36 · 7 · 832	Discriminant
Eigenvalues	2- 3- -2 7+  2  0 -4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-644,-6240]	[a1,a2,a3,a4,a6]
Generators	[-14:16:1]	Generators of the group modulo torsion
j	29540882258497/562473072	j-invariant
L	5.2476489040032	L(r)(E,1)/r!
Ω	0.94880467774994	Real period
R	0.46089999932404	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27888bd2 111552o2 10458k2 87150u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3486j2

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	+	2	0	-4	-8	-6	6	-8	10	-12	-2	-8	6	8	2	2	-4	4	-14	+	10	-8

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Quadratic twists for elliptic curve 3486j2

-4	8	-3	5	-7
27888bd2	111552o2	10458k2	87150u2	24402y2

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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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