Cremona's table of elliptic curves

583 = 11 · 53

Field	Data	Notes
Atkin-Lehner	11- 53+	Signs for the Atkin-Lehner involutions
Class	583b	Isogeny class
Conductor	583	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-2179708157 = -1 · 114 · 533	Discriminant
Eigenvalues	1 -1  4  4 11-  1  1 -3	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-358,-3595]	[a1,a2,a3,a4,a6]
j	-5096439860329/2179708157	j-invariant
L	2.1494927803175	L(r)(E,1)/r!
Ω	0.53737319507937	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	9328f1 37312g1 5247a1 14575f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 583b1

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	4	4	-	1	1	-3	5	-3	4	-3	10	-6	-10	+	-10	12	-4	3	-8	-7	-15	-6	-7

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Quadratic twists for elliptic curve 583b1

-4	8	-3	5	-7	-11	13	53
9328f1	37312g1	5247a1	14575f1	28567d1	6413h1	98527d1	30899b1

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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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