Cremona's table of elliptic curves

1008 = 2⁴ · 3² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 7-	Signs for the Atkin-Lehner involutions
Class	1008k	Isogeny class
Conductor	1008	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-51640810647552 = -1 · 212 · 37 · 78	Discriminant
Eigenvalues	2- 3-  2 7-  4 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4899,-370078]	[a1,a2,a3,a4,a6]
j	-4354703137/17294403	j-invariant
L	2.0836128058931	L(r)(E,1)/r!
Ω	0.26045160073663	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	63a6 4032bm6 336e6 25200dx5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008k6

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	-	4	-2	6	-4	0	2	0	6	-2	4	0	-6	12	-2	-4	0	-6	16	-12	14	18

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Quadratic twists for elliptic curve 1008k6

-4	8	-3	5	-7	-11
63a6	4032bm6	336e6	25200dx5	7056bx6	121968ec5

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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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