Cremona's table of elliptic curves

6897 = 3 · 11² · 19

Field	Data	Notes
Atkin-Lehner	3- 11- 19+	Signs for the Atkin-Lehner involutions
Class	6897d	Isogeny class
Conductor	6897	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-3608887659003 = -1 · 33 · 117 · 193	Discriminant
Eigenvalues	0 3-  0 -2 11-  1 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3637663,2669221561]	[a1,a2,a3,a4,a6]
Generators	[1085:907:1]	Generators of the group modulo torsion
j	-3004935183806464000/2037123	j-invariant
L	3.7789276492464	L(r)(E,1)/r!
Ω	0.48750395120383	Real period
R	0.6459653027623	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	110352bg2 20691m2 627b2	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 6897d2

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	-	0	-2	-	1	-3	+	6	0	8	2	-6	-8	-6	9	3	10	-10	-3	4	13	3	15	-10

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Quadratic twists for elliptic curve 6897d2

-4	-3	-11
110352bg2	20691m2	627b2

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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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