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	8470bb	Isogeny class
Conductor	8470	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	-1296968750 = -1 · 2 · 56 · 73 · 112	Discriminant
Eigenvalues	2-  1 5- 7+ 11- -5  0 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-140,-1858]	[a1,a2,a3,a4,a6]
j	-2509090441/10718750	j-invariant
L	3.7876315103929	L(r)(E,1)/r!
Ω	0.63127191839881	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	67760cj1 76230x1 42350y1 59290de1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470bb1

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	-	+	-	-5	0	-5	9	6	8	8	-6	10	0	6	-3	-2	-10	12	10	13	3	12	-10

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Quadratic twists for elliptic curve 8470bb1

-4	-3	5	-7	-11
67760cj1	76230x1	42350y1	59290de1	8470n1

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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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