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	8470l	Isogeny class
Conductor	8470	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-5548203757969180 = -1 · 22 · 5 · 76 · 119	Discriminant
Eigenvalues	2+ -2 5- 7+ 11- -2 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-10893,3609428]	[a1,a2,a3,a4,a6]
Generators	[-78:2035:1]	Generators of the group modulo torsion
j	-80677568161/3131816380	j-invariant
L	1.9410342528624	L(r)(E,1)/r!
Ω	0.35617375434198	Real period
R	1.3624208895237	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	67760cl3 76230dn3 42350cp3 59290v3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470l3

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	8	0	4	0	12	12	10	-4	-12	-14	10	0	-18	8

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Quadratic twists for elliptic curve 8470l3

-4	-3	5	-7	-11
67760cl3	76230dn3	42350cp3	59290v3	770g3

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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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