Cremona's table of elliptic curves

6890 = 2 · 5 · 13 · 53

Field	Data	Notes
Atkin-Lehner	2- 5- 13- 53-	Signs for the Atkin-Lehner involutions
Class	6890o	Isogeny class
Conductor	6890	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-563400069602500 = -1 · 22 · 54 · 134 · 534	Discriminant
Eigenvalues	2-  0 5- -4  0 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3443,1138489]	[a1,a2,a3,a4,a6]
Generators	[287:4926:1]	Generators of the group modulo torsion
j	4514950878012639/563400069602500	j-invariant
L	5.6707818284347	L(r)(E,1)/r!
Ω	0.39816768751902	Real period
R	1.7802743687494	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	55120x3 62010m3 34450a3 89570c3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890o4

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

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Quadratic twists for elliptic curve 6890o4

-4	-3	5	13
55120x3	62010m3	34450a3	89570c3

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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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