Cremona's table of elliptic curves

869 = 11 · 79

Field	Data	Notes
Atkin-Lehner	11- 79+	Signs for the Atkin-Lehner involutions
Class	869c	Isogeny class
Conductor	869	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	44	Modular degree for the optimal curve
Δ	-9559 = -1 · 112 · 79	Discriminant
Eigenvalues	-1 -2  2  4 11-  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2,-5]	[a1,a2,a3,a4,a6]
j	-912673/9559	j-invariant
L	0.86885759747143	L(r)(E,1)/r!
Ω	1.7377151949429	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	13904e1 55616c1 7821a1 21725c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 869c1

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	2	4	-	2	0	-4	0	0	4	2	0	4	2	2	-2	-4	12	10	-2	+	12	-6	14

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Quadratic twists for elliptic curve 869c1

-4	8	-3	5	-7	-11	-79
13904e1	55616c1	7821a1	21725c1	42581l1	9559c1	68651d1

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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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