Cremona's table of elliptic curves

583 = 11 · 53

Field	Data	Notes
Atkin-Lehner	11+ 53-	Signs for the Atkin-Lehner involutions
Class	583a	Isogeny class
Conductor	583	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-30899 = -1 · 11 · 532	Discriminant
Eigenvalues	2  1  3  0 11+  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,6,-5]	[a1,a2,a3,a4,a6]
j	20123648/30899	j-invariant
L	3.9230373200211	L(r)(E,1)/r!
Ω	1.9615186600105	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9328n1 37312m1 5247c1 14575c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 583a1

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	1	3	0	+	4	0	-4	-3	6	-3	7	-2	-2	0	-	5	0	7	3	-2	6	-10	-1	-7

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Quadratic twists for elliptic curve 583a1

-4	8	-3	5	-7	-11	13	53
9328n1	37312m1	5247c1	14575c1	28567b1	6413j1	98527n1	30899a1

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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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