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	8670z	Isogeny class
Conductor	8670	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	269280	Modular degree for the optimal curve
Δ	-154828331554483200 = -1 · 210 · 3 · 52 · 1710	Discriminant
Eigenvalues	2- 3- 5-  1  6  1 17+  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3342580,2351979152]	[a1,a2,a3,a4,a6]
j	-2048707405729/76800	j-invariant
L	6.0772420862057	L(r)(E,1)/r!
Ω	0.30386210431029	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	69360cq1 26010k1 43350e1 8670p1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670z1

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
-	-	-	1	6	1	+	7	-4	4	-3	5	-2	-5	4	2	-2	-1	-7	-12	-14	0	-10	-4	1

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Quadratic twists for elliptic curve 8670z1

-4	-3	5	17
69360cq1	26010k1	43350e1	8670p1

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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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