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	574h	Isogeny class
Conductor	574	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	-18368 = -1 · 26 · 7 · 41	Discriminant
Eigenvalues	2-  0 -4 7- -2 -6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,3,5]	[a1,a2,a3,a4,a6]
Generators	[1:2:1]	Generators of the group modulo torsion
j	4019679/18368	j-invariant
L	2.4117764640901	L(r)(E,1)/r!
Ω	2.7772218686004	Real period
R	0.5789422135259	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	4592c1 18368g1 5166t1 14350a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574h1

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
-	0	-4	-	-2	-6	-6	4	8	-8	0	-2	+	-8	0	0	2	-8	10	-12	10	16	-2	-10	-2

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Quadratic twists for elliptic curve 574h1

-4	8	-3	5	-7	-11	13	41
4592c1	18368g1	5166t1	14350a1	4018q1	69454d1	97006b1	23534s1

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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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