Cremona's table of elliptic curves

8200 = 2³ · 5² · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 41+	Signs for the Atkin-Lehner involutions
Class	8200g	Isogeny class
Conductor	8200	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-3800083392800000000 = -1 · 211 · 58 · 416	Discriminant
Eigenvalues	2-  0 5+ -2  4 -4 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-547675,182025750]	[a1,a2,a3,a4,a6]
j	-567730837600722/118752606025	j-invariant
L	0.95134428096317	L(r)(E,1)/r!
Ω	0.23783607024079	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16400a2 65600b2 73800y2 1640a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200g2

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
-	0	+	-2	4	-4	-2	-8	-4	4	4	6	+	-4	2	-12	-4	10	4	-6	-6	6	4	18	-10

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Quadratic twists for elliptic curve 8200g2

-4	8	-3	5
16400a2	65600b2	73800y2	1640a2

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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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