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	6853f	Isogeny class
Conductor	6853	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	6384	Modular degree for the optimal curve
Δ	-84983552731 = -1 · 72 · 117 · 89	Discriminant
Eigenvalues	0  0 -3 7+ 11-  3 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-6284,-192248]	[a1,a2,a3,a4,a6]
Generators	[100:423:1]	Generators of the group modulo torsion
j	-27443041428307968/84983552731	j-invariant
L	2.190435981796	L(r)(E,1)/r!
Ω	0.26805874452175	Real period
R	0.58367695955816	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	109648r1 61677b1 47971g1 75383e1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6853f1

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	-3	+	-	3	-4	-4	-4	5	10	4	1	-5	3	3	12	-5	12	-4	6	6	-11	-	1

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Quadratic twists for elliptic curve 6853f1

-4	-3	-7	-11
109648r1	61677b1	47971g1	75383e1

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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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