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	8200h	Isogeny class
Conductor	8200	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	4100000000 = 28 · 58 · 41	Discriminant
Eigenvalues	2- -2 5+ -2 -4 -4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5508,155488]	[a1,a2,a3,a4,a6]
Generators	[-38:558:1] [18:250:1]	Generators of the group modulo torsion
j	4620876496/1025	j-invariant
L	4.0419170830942	L(r)(E,1)/r!
Ω	1.351338819503	Real period
R	0.74776159479039	Regulator
r	2	Rank of the group of rational points
S	0.99999999999982	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16400c2 65600g2 73800w2 1640b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200h2

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

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Quadratic twists for elliptic curve 8200h2

-4	8	-3	5
16400c2	65600g2	73800w2	1640b2

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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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