Cremona's table of elliptic curves

8470 = 2 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	8470r	Isogeny class
Conductor	8470	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-8300600 = -1 · 23 · 52 · 73 · 112	Discriminant
Eigenvalues	2-  1 5+ 7+ 11-  1 -6  7	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-41,-175]	[a1,a2,a3,a4,a6]
Generators	[8:1:1]	Generators of the group modulo torsion
j	-63088729/68600	j-invariant
L	6.7402899260088	L(r)(E,1)/r!
Ω	0.90449253047056	Real period
R	1.2420021354409	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	67760bn1 76230bp1 42350w1 59290ei1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470r1

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	+	+	-	1	-6	7	3	-6	2	-4	0	4	-6	0	-3	-2	-4	0	4	-17	-9	-18	-10

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Quadratic twists for elliptic curve 8470r1

-4	-3	5	-7	-11
67760bn1	76230bp1	42350w1	59290ei1	8470i1

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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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