Cremona's table of elliptic curves

6552 = 2³ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	6552n	Isogeny class
Conductor	6552	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	-72935267781003264 = -1 · 211 · 39 · 77 · 133	Discriminant
Eigenvalues	2- 3+ -1 7+ -1 13-  3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,76437,10132614]	[a1,a2,a3,a4,a6]
Generators	[90:4212:1]	Generators of the group modulo torsion
j	1225217998314/1809323971	j-invariant
L	3.6951415932828	L(r)(E,1)/r!
Ω	0.23435253205652	Real period
R	2.6279081638651	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13104j1 52416a1 6552a1 45864y1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6552n1

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	-1	3	3	2	-5	-10	5	-8	-6	-6	9	8	-2	13	10	14	6	-18

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Quadratic twists for elliptic curve 6552n1

-4	8	-3	-7	13
13104j1	52416a1	6552a1	45864y1	85176h1

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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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