Cremona's table of elliptic curves

552 = 2³ · 3 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23-	Signs for the Atkin-Lehner involutions
Class	552d	Isogeny class
Conductor	552	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	7737043968 = 210 · 33 · 234	Discriminant
Eigenvalues	2- 3+  2 -4 -4 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-752,6972]	[a1,a2,a3,a4,a6]
Generators	[46:260:1]	Generators of the group modulo torsion
j	45989074372/7555707	j-invariant
L	1.8063895255896	L(r)(E,1)/r!
Ω	1.2581503271218	Real period
R	2.8715003074745	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1104c3 4416n3 1656a3 13800l3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 552d3

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	-4	-4	-2	-2	0	-	-2	0	-10	-6	8	-8	-6	-4	14	8	-8	-6	12	-12	-2	10

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Quadratic twists for elliptic curve 552d3

-4	8	-3	5	-7	-11	13	-23
1104c3	4416n3	1656a3	13800l3	27048v4	66792i4	93288g4	12696o3

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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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