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	574f	Isogeny class
Conductor	574	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	460816384 = 215 · 73 · 41	Discriminant
Eigenvalues	2+  1 -3 7-  0  2 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2335,-43598]	[a1,a2,a3,a4,a6]
Generators	[-28:17:1]	Generators of the group modulo torsion
j	1407074115849193/460816384	j-invariant
L	1.6140546542034	L(r)(E,1)/r!
Ω	0.68684485887238	Real period
R	0.78331840315596	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	4592i2 18368o2 5166bf2 14350o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574f2

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	-3	-	0	2	-3	-4	-6	-3	-1	-4	-	-1	-6	9	-6	-1	8	3	-10	-1	-12	3	-1

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Quadratic twists for elliptic curve 574f2

-4	8	-3	5	-7	-11	13	41
4592i2	18368o2	5166bf2	14350o2	4018c2	69454m2	97006h2	23534d2

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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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