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
deg	8160	Modular degree for the optimal curve
Δ	-9905620513718272 = -1 · 234 · 73 · 412	Discriminant
Eigenvalues	2+ -2  4 7-  4  4 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-31679,5254674]	[a1,a2,a3,a4,a6]
j	-3515753329334380009/9905620513718272	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	4592d1 18368h1 5166bm1 14350k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574d1

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 574d1

-4	8	-3	5	-7	-11	13	41
4592d1	18368h1	5166bm1	14350k1	4018g1	69454t1	97006m1	23534g1

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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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