Cremona's table of elliptic curves

7008 = 2⁵ · 3 · 73

Field	Data	Notes
Atkin-Lehner	2- 3- 73+	Signs for the Atkin-Lehner involutions
Class	7008j	Isogeny class
Conductor	7008	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	3405888 = 26 · 36 · 73	Discriminant
Eigenvalues	2- 3-  2  2 -6  0 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-42,-72]	[a1,a2,a3,a4,a6]
Generators	[-3:6:1]	Generators of the group modulo torsion
j	131096512/53217	j-invariant
L	5.4850161007829	L(r)(E,1)/r!
Ω	1.9391176436931	Real period
R	0.94287146847825	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	7008b1 14016f1 21024c1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7008j1

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	-6	0	-8	-4	0	6	10	-6	-10	-4	0	-10	6	14	4	-8	+	4	10	-14	2

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Quadratic twists for elliptic curve 7008j1

-4	8	-3
7008b1	14016f1	21024c1

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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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