Cremona's table of elliptic curves

8670 = 2 · 3 · 5 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	8670v	Isogeny class
Conductor	8670	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	401803628601600 = 28 · 32 · 52 · 178	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-393046,94807076]	[a1,a2,a3,a4,a6]
Generators	[-214:13112:1]	Generators of the group modulo torsion
j	278202094583041/16646400	j-invariant
L	6.9911882706549	L(r)(E,1)/r!
Ω	0.50471352733979	Real period
R	1.7314743641565	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	69360cb2 26010r2 43350b2 510e2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670v2

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

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Quadratic twists for elliptic curve 8670v2

-4	-3	5	17
69360cb2	26010r2	43350b2	510e2

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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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