Cremona's table of elliptic curves

4588 = 2² · 31 · 37

Field	Data	Notes
Atkin-Lehner	2- 31+ 37+	Signs for the Atkin-Lehner involutions
Class	4588a	Isogeny class
Conductor	4588	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	972	Modular degree for the optimal curve
Δ	-25123888 = -1 · 24 · 31 · 373	Discriminant
Eigenvalues	2-  0 -2  3 -6 -1  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,64,-139]	[a1,a2,a3,a4,a6]
j	1811939328/1570243	j-invariant
L	1.169255935073	L(r)(E,1)/r!
Ω	1.169255935073	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	18352k1 73408g1 41292a1 114700g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4588a1

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	-6	-1	6	-2	5	-1	+	+	-9	-7	13	6	0	9	-3	5	-8	-8	14	3	14

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Quadratic twists for elliptic curve 4588a1

-4	8	-3	5
18352k1	73408g1	41292a1	114700g1

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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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