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	6890n	Isogeny class
Conductor	6890	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-4747210 = -1 · 2 · 5 · 132 · 532	Discriminant
Eigenvalues	2-  2 5+  0 -4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,39,-31]	[a1,a2,a3,a4,a6]
Generators	[258:727:216]	Generators of the group modulo torsion
j	6549699311/4747210	j-invariant
L	7.5453895503505	L(r)(E,1)/r!
Ω	1.3702575248725	Real period
R	5.5065485234629	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	55120m2 62010t2 34450f2 89570j2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890n2

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

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Quadratic twists for elliptic curve 6890n2

-4	-3	5	13
55120m2	62010t2	34450f2	89570j2

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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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