Cremona's table of elliptic curves

8554 = 2 · 7 · 13 · 47

Field	Data	Notes
Atkin-Lehner	2+ 7+ 13- 47+	Signs for the Atkin-Lehner involutions
Class	8554a	Isogeny class
Conductor	8554	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-10897796 = -1 · 22 · 73 · 132 · 47	Discriminant
Eigenvalues	2+ -1  1 7+  3 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3657,-86663]	[a1,a2,a3,a4,a6]
j	-5411082280083481/10897796	j-invariant
L	1.2278146068778	L(r)(E,1)/r!
Ω	0.30695365171945	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	68432v1 76986ba1 59878f1 111202z1	Quadratic twists by: -4 -3 -7 13

Hecke Eigenvalues for elliptic curve 8554a1

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	+	3	-	2	2	0	10	8	-3	-1	1	+	5	-11	6	-12	6	3	6	-3	-14	10

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Quadratic twists for elliptic curve 8554a1

-4	-3	-7	13
68432v1	76986ba1	59878f1	111202z1

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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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