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	6	Product of Tamagawa factors cp
Δ	73668096 = 29 · 33 · 732	Discriminant
Eigenvalues	2- 3-  2  2 -6  0 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-312,1980]	[a1,a2,a3,a4,a6]
Generators	[15:30:1]	Generators of the group modulo torsion
j	6581255624/143883	j-invariant
L	5.4850161007829	L(r)(E,1)/r!
Ω	1.9391176436931	Real period
R	1.8857429369565	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	7008b2 14016f2 21024c2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7008j2

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 7008j2

-4	8	-3
7008b2	14016f2	21024c2

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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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