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	4588d	Isogeny class
Conductor	4588	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-652542064 = -1 · 24 · 313 · 372	Discriminant
Eigenvalues	2-  2 -1  3 -4 -6  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-126,-1303]	[a1,a2,a3,a4,a6]
Generators	[26:111:1]	Generators of the group modulo torsion
j	-13936624384/40783879	j-invariant
L	4.9442706319595	L(r)(E,1)/r!
Ω	0.6588675943609	Real period
R	1.2506990970256	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	18352o1 73408e1 41292c1 114700f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4588d1

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	-1	3	-4	-6	0	5	0	0	+	-	-9	-2	-4	0	-1	-8	12	-3	4	12	8	-16	-9

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Quadratic twists for elliptic curve 4588d1

-4	8	-3	5
18352o1	73408e1	41292c1	114700f1

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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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