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	574b	Isogeny class
Conductor	574	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	100803584 = 210 · 74 · 41	Discriminant
Eigenvalues	2+  2 -2 7+ -6 -4 -2  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2061,35165]	[a1,a2,a3,a4,a6]
Generators	[17:65:1]	Generators of the group modulo torsion
j	968917714969177/100803584	j-invariant
L	1.8100407779088	L(r)(E,1)/r!
Ω	1.8130899301799	Real period
R	0.99831825646358	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4592k1 18368c1 5166bc1 14350s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574b1

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	-2	+	-6	-4	-2	2	0	0	0	10	+	4	8	-4	-8	10	-14	-12	-6	0	4	-14	-10

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Quadratic twists for elliptic curve 574b1

-4	8	-3	5	-7	-11	13	41
4592k1	18368c1	5166bc1	14350s1	4018h1	69454ba1	97006u1	23534m1

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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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