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	552a	Isogeny class
Conductor	552	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-17169408 = -1 · 210 · 36 · 23	Discriminant
Eigenvalues	2+ 3+ -2  2 -2 -2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-64,-260]	[a1,a2,a3,a4,a6]
Generators	[18:64:1]	Generators of the group modulo torsion
j	-28756228/16767	j-invariant
L	1.7081772832086	L(r)(E,1)/r!
Ω	0.82085418637744	Real period
R	2.0809752956821	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1104e1 4416g1 1656h1 13800y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 552a1

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	-2	-2	-4	0	+	-10	0	-4	-6	-4	8	-6	4	8	-4	8	6	6	-6	-4	10

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Quadratic twists for elliptic curve 552a1

-4	8	-3	5	-7	-11	13	-23
1104e1	4416g1	1656h1	13800y1	27048g1	66792x1	93288w1	12696d1

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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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