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	6552i	Isogeny class
Conductor	6552	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-832156416 = -1 · 28 · 36 · 73 · 13	Discriminant
Eigenvalues	2+ 3-  1 7- -4 13+  6  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,-1388]	[a1,a2,a3,a4,a6]
Generators	[26:126:1]	Generators of the group modulo torsion
j	-1024/4459	j-invariant
L	4.3635888513097	L(r)(E,1)/r!
Ω	0.71998431261622	Real period
R	0.25252800505782	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	13104m1 52416cy1 728d1 45864s1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6552i1

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	-	-4	+	6	1	-1	-3	-7	-10	10	-7	9	-3	0	6	-6	-10	-11	-3	-11	7	17

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Quadratic twists for elliptic curve 6552i1

-4	8	-3	-7	13
13104m1	52416cy1	728d1	45864s1	85176bs1

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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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