Cremona's table of elliptic curves

6572 = 2² · 31 · 53

Field	Data	Notes
Atkin-Lehner	2- 31+ 53+	Signs for the Atkin-Lehner involutions
Class	6572a	Isogeny class
Conductor	6572	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1632	Modular degree for the optimal curve
Δ	-13038848 = -1 · 28 · 312 · 53	Discriminant
Eigenvalues	2- -1  0 -4 -2 -1 -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-388,3080]	[a1,a2,a3,a4,a6]
Generators	[-22:22:1] [-2:62:1]	Generators of the group modulo torsion
j	-25298674000/50933	j-invariant
L	4.2051571317878	L(r)(E,1)/r!
Ω	2.2449611811152	Real period
R	0.31219226767055	Regulator
r	2	Rank of the group of rational points
S	0.99999999999987	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	26288f1 105152f1 59148g1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6572a1

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	0	-4	-2	-1	-5	-1	-3	-9	+	3	-12	6	-12	+	-10	12	12	-7	-4	-11	-15	-2	-7

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Quadratic twists for elliptic curve 6572a1

-4	8	-3
26288f1	105152f1	59148g1

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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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