Cremona's table of elliptic curves

9583 = 7 · 37²

Field	Data	Notes
Atkin-Lehner	7+ 37-	Signs for the Atkin-Lehner involutions
Class	9583a	Isogeny class
Conductor	9583	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-17373979 = -1 · 73 · 373	Discriminant
Eigenvalues	0  2  3 7+  3  3  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-49,257]	[a1,a2,a3,a4,a6]
j	-262144/343	j-invariant
L	3.9515926598605	L(r)(E,1)/r!
Ω	1.9757963299303	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	86247k1 67081h1 9583b1	Quadratic twists by: -3 -7 37

Hecke Eigenvalues for elliptic curve 9583a1

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
0	2	3	+	3	3	6	0	6	6	3	-	0	-12	-6	9	-3	6	-13	3	2	12	6	-9	-15

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Quadratic twists for elliptic curve 9583a1

-3	-7	37
86247k1	67081h1	9583b1

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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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