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	3486r	Isogeny class
Conductor	3486	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-1377444096 = -1 · 28 · 33 · 74 · 83	Discriminant
Eigenvalues	2- 3- -3 7- -5 -2  8 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,273,441]	[a1,a2,a3,a4,a6]
Generators	[0:21:1]	Generators of the group modulo torsion
j	2249635843727/1377444096	j-invariant
L	5.0725825604019	L(r)(E,1)/r!
Ω	0.93711410137769	Real period
R	0.056385238033631	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27888r1 111552v1 10458o1 87150e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3486r1

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
-	-	-3	-	-5	-2	8	-5	3	-4	-6	-1	-2	-12	0	1	-11	7	-11	-12	4	-12	-	11	-14

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Quadratic twists for elliptic curve 3486r1

-4	8	-3	5	-7
27888r1	111552v1	10458o1	87150e1	24402v1

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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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