Cremona's table of elliptic curves

6889 = 83²

Field	Data	Notes
Atkin-Lehner	83-	Signs for the Atkin-Lehner involutions
Class	6889a	Isogeny class
Conductor	6889	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	13776	Modular degree for the optimal curve
Δ	-27136050989627 = -1 · 837	Discriminant
Eigenvalues	1 -1  2 -3  3  6  5 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,6746,134507]	[a1,a2,a3,a4,a6]
j	103823/83	j-invariant
L	1.7186135367786	L(r)(E,1)/r!
Ω	0.42965338419465	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	110224k1 62001k1 83a1	Quadratic twists by: -4 -3 -83

Hecke Eigenvalues for elliptic curve 6889a1

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
1	-1	2	-3	3	6	5	-2	-4	-7	5	-11	-2	8	0	-6	5	5	2	-2	0	-14	-	0	8

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Quadratic twists for elliptic curve 6889a1

-4	-3	-83
110224k1	62001k1	83a1

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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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