Cremona's table of elliptic curves

583 = 11 · 53

Field	Data	Notes
Atkin-Lehner	11- 53+	Signs for the Atkin-Lehner involutions
Class	583c	Isogeny class
Conductor	583	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1248	Modular degree for the optimal curve
Δ	-10502230211 = -1 · 113 · 534	Discriminant
Eigenvalues	2  3 -3  2 11-  0  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,491,-2603]	[a1,a2,a3,a4,a6]
j	13090860306432/10502230211	j-invariant
L	4.2757149187562	L(r)(E,1)/r!
Ω	0.71261915312603	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	9328h1 37312k1 5247b1 14575g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 583c1

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	3	-3	2	-	0	6	-8	-5	-4	-5	11	12	-2	-8	+	13	-8	-3	1	-4	-10	2	7	1

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Quadratic twists for elliptic curve 583c1

-4	8	-3	5	-7	-11	13	53
9328h1	37312k1	5247b1	14575g1	28567e1	6413i1	98527f1	30899d1

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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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