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	8470u	Isogeny class
Conductor	8470	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-3785996266995712000 = -1 · 218 · 53 · 72 · 119	Discriminant
Eigenvalues	2- -2 5+ 7+ 11- -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,274849,-75395495]	[a1,a2,a3,a4,a6]
Generators	[384:9125:1]	Generators of the group modulo torsion
j	1296134247276791/2137096192000	j-invariant
L	3.9396775560964	L(r)(E,1)/r!
Ω	0.13087780575325	Real period
R	0.83616536080737	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	67760bs3 76230bt3 42350ba3 59290eo3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470u3

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	+	+	-	-2	6	-2	-6	0	8	-4	-12	4	12	0	0	-2	8	12	-2	-14	-12	6	8

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Quadratic twists for elliptic curve 8470u3

-4	-3	5	-7	-11
67760bs3	76230bt3	42350ba3	59290eo3	770b3

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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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