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	1632955059363690000 = 24 · 34 · 54 · 1710	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-416166,83020500]	[a1,a2,a3,a4,a6]
Generators	[-222:12936:1]	Generators of the group modulo torsion
j	330240275458561/67652010000	j-invariant
L	6.9911882706549	L(r)(E,1)/r!
Ω	0.2523567636699	Real period
R	3.462948728313	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	69360cb3 26010r3 43350b3 510e3	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670v3

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 8670v3

-4	-3	5	17
69360cb3	26010r3	43350b3	510e3

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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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