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	574d	Isogeny class
Conductor	574	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	43574618474283008 = 217 · 76 · 414	Discriminant
Eigenvalues	2+ -2  4 7-  4  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-687039,218902034]	[a1,a2,a3,a4,a6]
j	35864681248144538691049/43574618474283008	j-invariant
L	1.0784518611177	L(r)(E,1)/r!
Ω	0.35948395370591	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4592d2 18368h2 5166bm2 14350k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574d2

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
+	-2	4	-	4	4	-2	-6	-8	6	4	2	+	0	4	2	14	4	-8	8	-14	-8	6	10	6

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Quadratic twists for elliptic curve 574d2

-4	8	-3	5	-7	-11	13	41
4592d2	18368h2	5166bm2	14350k2	4018g2	69454t2	97006m2	23534g2

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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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