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	8200c	Isogeny class
Conductor	8200	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	102500000000 = 28 · 510 · 41	Discriminant
Eigenvalues	2+  0 5+  0  4 -6  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1175,-1750]	[a1,a2,a3,a4,a6]
j	44851536/25625	j-invariant
L	1.7661995021753	L(r)(E,1)/r!
Ω	0.88309975108764	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	16400g1 65600n1 73800bz1 1640g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200c1

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	+	0	4	-6	2	4	8	-6	8	-6	-	-4	0	-6	12	6	-8	4	6	4	-12	-14	10

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Quadratic twists for elliptic curve 8200c1

-4	8	-3	5
16400g1	65600n1	73800bz1	1640g1

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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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