Cremona's table of elliptic curves

2988 = 2² · 3² · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 83-	Signs for the Atkin-Lehner involutions
Class	2988c	Isogeny class
Conductor	2988	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	34712623872 = 28 · 39 · 832	Discriminant
Eigenvalues	2- 3- -4  4 -4 -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1047,9470]	[a1,a2,a3,a4,a6]
j	680136784/186003	j-invariant
L	1.084000848956	L(r)(E,1)/r!
Ω	1.084000848956	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	11952r2 47808r2 996a2 74700i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2988c2

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

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Quadratic twists for elliptic curve 2988c2

-4	8	-3	5
11952r2	47808r2	996a2	74700i2

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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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