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	574j	Isogeny class
Conductor	574	Conductor
∏ cp	25	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	22050784 = 25 · 75 · 41	Discriminant
Eigenvalues	2- -1  1 7-  2  4  3  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-175,789]	[a1,a2,a3,a4,a6]
j	592915705201/22050784	j-invariant
L	2.1296506457988	L(r)(E,1)/r!
Ω	2.1296506457988	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	4592h1 18368n1 5166p1 14350d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 574j1

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
-	-1	1	-	2	4	3	0	4	-5	7	-2	-	-1	-2	-1	10	-13	-2	-3	4	-15	-6	-15	-7

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Quadratic twists for elliptic curve 574j1

-4	8	-3	5	-7	-11	13	41
4592h1	18368n1	5166p1	14350d1	4018n1	69454a1	97006a1	23534t1

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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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