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	8866f	Isogeny class
Conductor	8866	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-13946218 = -1 · 2 · 113 · 132 · 31	Discriminant
Eigenvalues	2+ -2 -2 -3 11- 13+ -5  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-367,2676]	[a1,a2,a3,a4,a6]
Generators	[-14:78:1] [-8:75:1]	Generators of the group modulo torsion
j	-5445273626857/13946218	j-invariant
L	2.7989265766816	L(r)(E,1)/r!
Ω	2.235843942825	Real period
R	0.20864057363099	Regulator
r	2	Rank of the group of rational points
S	0.99999999999973	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70928g1 79794s1 97526ba1 115258m1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 8866f1

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
+	-2	-2	-3	-	+	-5	4	-5	4	+	-1	0	-1	-12	6	-5	-8	-11	0	-10	-10	9	-4	-5

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Quadratic twists for elliptic curve 8866f1

-4	-3	-11	13
70928g1	79794s1	97526ba1	115258m1

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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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