Cremona's table of elliptic curves

588 = 2² · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+	Signs for the Atkin-Lehner involutions
Class	588a	Isogeny class
Conductor	588	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-149361408 = -1 · 28 · 35 · 74	Discriminant
Eigenvalues	2- 3+ -2 7+  2 -3  8 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,131,-167]	[a1,a2,a3,a4,a6]
j	401408/243	j-invariant
L	1.0627828254011	L(r)(E,1)/r!
Ω	1.0627828254011	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	2352s1 9408w1 1764d1 14700z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 588a1

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

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Quadratic twists for elliptic curve 588a1

-4	8	-3	5	-7	-11	13
2352s1	9408w1	1764d1	14700z1	588d1	71148i1	99372a1

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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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