Cremona's table of elliptic curves

574 = 2 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	574g	Isogeny class
Conductor	574	Conductor
∏ cp	11	Product of Tamagawa factors cp
deg	88	Modular degree for the optimal curve
Δ	587776 = 211 · 7 · 41	Discriminant
Eigenvalues	2- -1 -1 7+ -6 -4  7  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-21,-5]	[a1,a2,a3,a4,a6]
Generators	[-1:4:1]	Generators of the group modulo torsion
j	1027243729/587776	j-invariant
L	2.3048347394264	L(r)(E,1)/r!
Ω	2.485463955045	Real period
R	0.084302341392495	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	4592l1 18368d1 5166h1 14350e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574g1

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	+	-6	-4	7	0	-8	1	5	-2	-	-5	-6	-3	-10	-3	14	3	8	7	-2	5	5

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Quadratic twists for elliptic curve 574g1

-4	8	-3	5	-7	-11	13	41
4592l1	18368d1	5166h1	14350e1	4018m1	69454g1	97006g1	23534v1

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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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