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	574i	Isogeny class
Conductor	574	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	10906239337336 = 23 · 7 · 417	Discriminant
Eigenvalues	2- -3 -1 7- -2  0 -3 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-9611313,-11466507927]	[a1,a2,a3,a4,a6]
Generators	[-6040065:3021062:3375]	Generators of the group modulo torsion
j	98191033604529537629349729/10906239337336	j-invariant
L	1.9219551259947	L(r)(E,1)/r!
Ω	0.085744027315956	Real period
R	7.4716773718149	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	4592f2 18368j2 5166r2 14350b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574i2

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
-	-3	-1	-	-2	0	-3	-8	-4	-5	-3	10	+	-5	6	-9	-10	13	-2	9	4	-11	-14	-1	7

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Quadratic twists for elliptic curve 574i2

-4	8	-3	5	-7	-11	13	41
4592f2	18368j2	5166r2	14350b2	4018s2	69454e2	97006e2	23534u2

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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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