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	8670l	Isogeny class
Conductor	8670	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	290304	Modular degree for the optimal curve
Δ	-1.9996320102439E+19	Discriminant
Eigenvalues	2+ 3- 5- -2  4  4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-772648,338494838]	[a1,a2,a3,a4,a6]
Generators	[-758:22487:1]	Generators of the group modulo torsion
j	-2113364608155289/828431400960	j-invariant
L	4.1317131552688	L(r)(E,1)/r!
Ω	0.20319366912943	Real period
R	1.452419110782	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	69360ct1 26010bk1 43350cb1 510a1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 8670l1

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	4	4	+	-4	-8	-2	-4	-6	-8	6	8	-2	-6	-14	-2	-2	-4	0	-16	-2	0

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Quadratic twists for elliptic curve 8670l1

-4	-3	5	17
69360ct1	26010bk1	43350cb1	510a1

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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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