Cremona's table of elliptic curves

8866 = 2 · 11 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 11- 13- 31-	Signs for the Atkin-Lehner involutions
Class	8866k	Isogeny class
Conductor	8866	Conductor
∏ cp	440	Product of Tamagawa factors cp
deg	133760	Modular degree for the optimal curve
Δ	-10698942220888064 = -1 · 211 · 114 · 135 · 312	Discriminant
Eigenvalues	2-  1 -1 -5 11- 13-  3  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-426021,107107457]	[a1,a2,a3,a4,a6]
Generators	[2422:114047:1]	Generators of the group modulo torsion
j	-8550997869217196107729/10698942220888064	j-invariant
L	6.2135790923841	L(r)(E,1)/r!
Ω	0.40422549641299	Real period
R	0.034935378371287	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	70928i1 79794h1 97526g1 115258a1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 8866k1

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	-5	-	-	3	6	6	-2	-	9	-6	3	-5	-14	-8	-10	-8	-3	-10	4	-8	12	2

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Quadratic twists for elliptic curve 8866k1

-4	-3	-11	13
70928i1	79794h1	97526g1	115258a1

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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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