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	4588g	Isogeny class
Conductor	4588	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-679024 = -1 · 24 · 31 · 372	Discriminant
Eigenvalues	2-  0 -1 -5 -4 -4 -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,7,-39]	[a1,a2,a3,a4,a6]
Generators	[5:11:1] [11:37:1]	Generators of the group modulo torsion
j	2370816/42439	j-invariant
L	3.9984812232207	L(r)(E,1)/r!
Ω	1.3971788052675	Real period
R	0.47697083200159	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18352h1 73408h1 41292j1 114700i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4588g1

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	-1	-5	-4	-4	-2	1	-2	-6	-	-	3	-12	8	-12	-9	-6	-4	-7	12	-10	16	2	-17

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Quadratic twists for elliptic curve 4588g1

-4	8	-3	5
18352h1	73408h1	41292j1	114700i1

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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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