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	588c	Isogeny class
Conductor	588	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	16464 = 24 · 3 · 73	Discriminant
Eigenvalues	2- 3+ -2 7-  2  4 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9,-6]	[a1,a2,a3,a4,a6]
Generators	[-1:1:1]	Generators of the group modulo torsion
j	16384/3	j-invariant
L	1.7240643601518	L(r)(E,1)/r!
Ω	2.7659029545926	Real period
R	0.41555190437638	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	2352w1 9408bf1 1764g1 14700bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 588c1

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	4	-6	-8	-6	-10	-4	6	6	4	-8	2	4	8	-8	-10	-4	4	-12	14	-4

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Quadratic twists for elliptic curve 588c1

-4	8	-3	5	-7	-11	13
2352w1	9408bf1	1764g1	14700bg1	588e1	71148w1	99372o1

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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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