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	1008d	Isogeny class
Conductor	1008	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	48384 = 28 · 33 · 7	Discriminant
Eigenvalues	2+ 3+ -2 7-  2  2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-111,-450]	[a1,a2,a3,a4,a6]
j	21882096/7	j-invariant
L	1.4708796770573	L(r)(E,1)/r!
Ω	1.4708796770573	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	504a2 4032x2 1008c2 25200b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1008d2

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	2	-6	4	6	0	4	10	-2	4	4	12	12	6	4	-14	-2	8	-16	6	-18

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Quadratic twists for elliptic curve 1008d2

-4	8	-3	5	-7	-11
504a2	4032x2	1008c2	25200b2	7056g2	121968h2

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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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