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	12	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-2490394032 = -1 · 24 · 33 · 78	Discriminant
Eigenvalues	2- 3+  0 7- -6 -2  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,327,666]	[a1,a2,a3,a4,a6]
Generators	[5:49:1]	Generators of the group modulo torsion
j	2048000/1323	j-invariant
L	1.8046862614269	L(r)(E,1)/r!
Ω	0.90328904586673	Real period
R	0.66596854007576	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	2352t1 9408bb1 1764f1 14700bn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 588b1

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 588b1

-4	8	-3	5	-7	-11	13
2352t1	9408bb1	1764f1	14700bn1	84a1	71148n1	99372g1

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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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