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	8200k	Isogeny class
Conductor	8200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	164000000 = 28 · 56 · 41	Discriminant
Eigenvalues	2- -2 5+  2  2 -6  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-308,1888]	[a1,a2,a3,a4,a6]
Generators	[-2:50:1]	Generators of the group modulo torsion
j	810448/41	j-invariant
L	3.0940563965177	L(r)(E,1)/r!
Ω	1.7922120215632	Real period
R	0.43159742810718	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	16400j1 65600u1 73800o1 328b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200k1

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

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Quadratic twists for elliptic curve 8200k1

-4	8	-3	5
16400j1	65600u1	73800o1	328b1

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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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