Cremona's table of elliptic curves

869 = 11 · 79

Field	Data	Notes
Atkin-Lehner	11- 79-	Signs for the Atkin-Lehner involutions
Class	869d	Isogeny class
Conductor	869	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	59657719 = 112 · 793	Discriminant
Eigenvalues	1 -1  1  1 11-  1 -8  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-512,4237]	[a1,a2,a3,a4,a6]
Generators	[-4:81:1]	Generators of the group modulo torsion
j	14888751553801/59657719	j-invariant
L	2.5742151775337	L(r)(E,1)/r!
Ω	1.9846117143677	Real period
R	0.21618126095712	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	13904c1 55616f1 7821b1 21725d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 869d1

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	-1	1	1	-	1	-8	0	-4	6	-8	0	-8	-12	-1	6	5	-6	2	-9	10	-	6	-3	17

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Quadratic twists for elliptic curve 869d1

-4	8	-3	5	-7	-11	-79
13904c1	55616f1	7821b1	21725d1	42581n1	9559a1	68651c1

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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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