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	8866c	Isogeny class
Conductor	8866	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	102144	Modular degree for the optimal curve
Δ	-342782144042624 = -1 · 27 · 118 · 13 · 312	Discriminant
Eigenvalues	2+ -3  3  3 11+ 13+  7  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,16247,393613]	[a1,a2,a3,a4,a6]
j	474272799173478423/342782144042624	j-invariant
L	1.3733375323733	L(r)(E,1)/r!
Ω	0.34333438309331	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70928k1 79794bb1 97526be1 115258s1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 8866c1

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
+	-3	3	3	+	+	7	0	8	-6	-	-7	-4	11	3	-4	-8	10	2	9	-10	-2	-2	10	16

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Quadratic twists for elliptic curve 8866c1

-4	-3	-11	13
70928k1	79794bb1	97526be1	115258s1

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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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