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	8866b	Isogeny class
Conductor	8866	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	13728	Modular degree for the optimal curve
Δ	-118024192 = -1 · 211 · 11 · 132 · 31	Discriminant
Eigenvalues	2+  0  0  3 11+ 13+  1  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-53537,-4754563]	[a1,a2,a3,a4,a6]
j	-16970333195884811625/118024192	j-invariant
L	1.255439121164	L(r)(E,1)/r!
Ω	0.1569298901455	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	70928j1 79794ba1 97526bc1 115258p1	Quadratic twists by: -4 -3 -11 13

Hecke Eigenvalues for elliptic curve 8866b1

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
+	0	0	3	+	+	1	0	-1	6	-	-7	2	-1	-6	2	13	10	11	6	-10	-14	-11	10	7

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Quadratic twists for elliptic curve 8866b1

-4	-3	-11	13
70928j1	79794ba1	97526bc1	115258p1

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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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