Cremona's table of elliptic curves

8008 = 2³ · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 7- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	8008a	Isogeny class
Conductor	8008	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	352512	Modular degree for the optimal curve
Δ	-843936059110144 = -1 · 28 · 7 · 118 · 133	Discriminant
Eigenvalues	2+ -2 -1 7- 11+ 13+ -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-36613281,-85284134429]	[a1,a2,a3,a4,a6]
j	-21203116761178214318777344/3296625230899	j-invariant
L	0.24549908783997	L(r)(E,1)/r!
Ω	0.030687385979996	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16016b1 64064t1 72072bm1 56056e1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8008a1

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	-1	-	+	+	-6	-7	1	-5	-7	-2	6	1	7	-13	0	6	-14	-6	-3	-11	-13	9	17

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Quadratic twists for elliptic curve 8008a1

-4	8	-3	-7	-11	13
16016b1	64064t1	72072bm1	56056e1	88088z1	104104r1

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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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