Cremona's table of elliptic curves

82369 = 7² · 41²

Field	Data	Notes
Atkin-Lehner	7- 41+	Signs for the Atkin-Lehner involutions
Class	82369a	Isogeny class
Conductor	82369	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1629285754663 = 73 · 416	Discriminant
Eigenvalues	1  0  0 7- -4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-62512,-5999883]	[a1,a2,a3,a4,a6]
j	16581375	j-invariant
L	0.30193254574328	L(r)(E,1)/r!
Ω	0.30193256196945	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	82369a4 49a2	Quadratic twists by: -7 41

Hecke Eigenvalues for elliptic curve 82369a2

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
1	0	0	-	-4	0	0	0	8	-2	0	-6	+	-12	0	10	0	0	-4	-16	0	-8	0	0	0

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Quadratic twists for elliptic curve 82369a2

-7	41
82369a4	49a2

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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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