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	574i	Isogeny class
Conductor	574	Conductor
∏ cp	147	Product of Tamagawa factors cp
deg	3528	Modular degree for the optimal curve
Δ	70810888830976 = 221 · 77 · 41	Discriminant
Eigenvalues	2- -3 -1 7- -2  0 -3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-19353,958713]	[a1,a2,a3,a4,a6]
Generators	[-121:1292:1]	Generators of the group modulo torsion
j	801581275315909089/70810888830976	j-invariant
L	1.9219551259947	L(r)(E,1)/r!
Ω	0.60020819121169	Real period
R	1.0673824816878	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	7	Number of elements in the torsion subgroup
Twists	4592f1 18368j1 5166r1 14350b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574i1

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
-	-3	-1	-	-2	0	-3	-8	-4	-5	-3	10	+	-5	6	-9	-10	13	-2	9	4	-11	-14	-1	7

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Quadratic twists for elliptic curve 574i1

-4	8	-3	5	-7	-11	13	41
4592f1	18368j1	5166r1	14350b1	4018s1	69454e1	97006e1	23534u1

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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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