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	588b	Isogeny class
Conductor	588	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	153692888832 = 28 · 36 · 77	Discriminant
Eigenvalues	2- 3+  0 7- -6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1388,6840]	[a1,a2,a3,a4,a6]
Generators	[-2:98:1]	Generators of the group modulo torsion
j	9826000/5103	j-invariant
L	1.8046862614269	L(r)(E,1)/r!
Ω	0.90328904586673	Real period
R	0.33298427003788	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2352t2 9408bb2 1764f2 14700bn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 588b2

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	-	-6	-2	0	4	-6	6	-8	2	-12	-4	-12	-6	0	10	8	6	10	-4	12	-12	10

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Quadratic twists for elliptic curve 588b2

-4	8	-3	5	-7	-11	13
2352t2	9408bb2	1764f2	14700bn2	84a2	71148n2	99372g2

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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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