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	6552g	Isogeny class
Conductor	6552	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-2870090496 = -1 · 28 · 36 · 7 · 133	Discriminant
Eigenvalues	2+ 3-  1 7+ -2 13-  0 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-612,6372]	[a1,a2,a3,a4,a6]
Generators	[42:234:1]	Generators of the group modulo torsion
j	-135834624/15379	j-invariant
L	4.1348234988264	L(r)(E,1)/r!
Ω	1.3912406118955	Real period
R	0.12383502248139	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	13104z1 52416bn1 728c1 45864j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6552g1

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	+	-2	-	0	-7	3	9	5	-8	10	5	-7	-3	0	6	-10	-4	-11	-11	-11	3	-15

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Quadratic twists for elliptic curve 6552g1

-4	8	-3	-7	13
13104z1	52416bn1	728c1	45864j1	85176ca1

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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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