Cremona's table of elliptic curves

6853 = 7 · 11 · 89

Field	Data	Notes
Atkin-Lehner	7+ 11- 89-	Signs for the Atkin-Lehner involutions
Class	6853g	Isogeny class
Conductor	6853	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	4269419 = 72 · 11 · 892	Discriminant
Eigenvalues	-1  0 -2 7+ 11- -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-46,-54]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1]	Generators of the group modulo torsion
j	10546683057/4269419	j-invariant
L	1.7984410723448	L(r)(E,1)/r!
Ω	1.9022052761348	Real period
R	0.94545057513412	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	109648q2 61677c2 47971j2 75383g2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6853g2

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	0	-2	+	-	-2	0	4	-6	8	4	-6	-10	8	6	-6	0	2	12	4	4	0	12	-	-10

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Quadratic twists for elliptic curve 6853g2

-4	-3	-7	-11
109648q2	61677c2	47971j2	75383g2

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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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