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	6890c	Isogeny class
Conductor	6890	Conductor
∏ cp	7	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	-107656250 = -1 · 2 · 57 · 13 · 53	Discriminant
Eigenvalues	2+  1 5- -2  4 13+ -2  3	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-133,-782]	[a1,a2,a3,a4,a6]
Generators	[14:5:1]	Generators of the group modulo torsion
j	-257380823881/107656250	j-invariant
L	3.6347711858076	L(r)(E,1)/r!
Ω	0.68943965139961	Real period
R	0.75315225268785	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	55120p1 62010bm1 34450r1 89570s1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 6890c1

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	-	-2	4	+	-2	3	6	-8	0	-6	-7	8	-4	-	0	-15	-8	4	4	0	0	-10	-5

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Quadratic twists for elliptic curve 6890c1

-4	-3	5	13
55120p1	62010bm1	34450r1	89570s1

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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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