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	72	Product of Tamagawa factors cp
Δ	1.7575198909638E+20	Discriminant
Eigenvalues	2- -2 5+ 7+ 11- -2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1893471,-774028199]	[a1,a2,a3,a4,a6]
Generators	[-804:15527:1]	Generators of the group modulo torsion
j	423783056881319689/99207416000000	j-invariant
L	3.9396775560964	L(r)(E,1)/r!
Ω	0.13087780575325	Real period
R	1.6723307216147	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	67760bs4 76230bt4 42350ba4 59290eo4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470u4

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 8470u4

-4	-3	5	-7	-11
67760bs4	76230bt4	42350ba4	59290eo4	770b4

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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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