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	6552o	Isogeny class
Conductor	6552	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-3577392 = -1 · 24 · 33 · 72 · 132	Discriminant
Eigenvalues	2- 3+  0 7-  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-90,341]	[a1,a2,a3,a4,a6]
Generators	[2:13:1]	Generators of the group modulo torsion
j	-186624000/8281	j-invariant
L	4.1926822637594	L(r)(E,1)/r!
Ω	2.4740946062296	Real period
R	0.42365823978624	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	13104a1 52416ba1 6552b1 45864ba1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6552o1

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	+	2	-4	2	-4	0	6	-4	4	-6	4	-10	-10	8	-8	2	-8	-2	-16	14

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Quadratic twists for elliptic curve 6552o1

-4	8	-3	-7	13
13104a1	52416ba1	6552b1	45864ba1	85176a1

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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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