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	8200a	Isogeny class
Conductor	8200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	52531250000 = 24 · 59 · 412	Discriminant
Eigenvalues	2+  2 5+  2  0  0 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1383,-15988]	[a1,a2,a3,a4,a6]
Generators	[-134:375:8]	Generators of the group modulo torsion
j	1171019776/210125	j-invariant
L	6.1762485379248	L(r)(E,1)/r!
Ω	0.7924813998824	Real period
R	1.9483891164011	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	16400f1 65600i1 73800cj1 1640f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8200a1

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

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Quadratic twists for elliptic curve 8200a1

-4	8	-3	5
16400f1	65600i1	73800cj1	1640f1

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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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