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	7008f	Isogeny class
Conductor	7008	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-24556032 = -1 · 29 · 32 · 732	Discriminant
Eigenvalues	2+ 3-  0 -2  0  4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,72,72]	[a1,a2,a3,a4,a6]
Generators	[3:18:1]	Generators of the group modulo torsion
j	79507000/47961	j-invariant
L	4.7257055497878	L(r)(E,1)/r!
Ω	1.3048923887312	Real period
R	1.8107644701579	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	7008i2 14016k2 21024l2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 7008f2

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
+	-	0	-2	0	4	-6	4	-8	0	6	10	-10	8	-10	-4	0	-10	4	12	-	0	-8	-10	-14

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Quadratic twists for elliptic curve 7008f2

-4	8	-3
7008i2	14016k2	21024l2

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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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