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	1008h	Isogeny class
Conductor	1008	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3584673792 = 211 · 36 · 74	Discriminant
Eigenvalues	2+ 3- -2 7- -4  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-531,-3726]	[a1,a2,a3,a4,a6]
Generators	[-11:28:1]	Generators of the group modulo torsion
j	11090466/2401	j-invariant
L	2.2980532163643	L(r)(E,1)/r!
Ω	1.0098414092319	Real period
R	0.28445719240611	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	504c4 4032bj3 112b4 25200bf3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008h3

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	-8	0	-6	-8	-2	-2	4	-8	-6	0	-6	4	-8	10	-16	8	6	-6

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Quadratic twists for elliptic curve 1008h3

-4	8	-3	5	-7	-11
504c4	4032bj3	112b4	25200bf3	7056x4	121968bl3

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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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