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	8470ba	Isogeny class
Conductor	8470	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	1123396628679710000 = 24 · 54 · 78 · 117	Discriminant
Eigenvalues	2-  0 5- 7+ 11-  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-264892,-12309041]	[a1,a2,a3,a4,a6]
j	1160306142246441/634128110000	j-invariant
L	3.5957867446109	L(r)(E,1)/r!
Ω	0.22473667153818	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67760cg3 76230y3 42350u3 59290cv3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470ba3

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
-	0	-	+	-	6	2	4	-4	-6	0	-2	6	4	4	-2	12	2	-8	-8	10	8	12	10	-6

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Quadratic twists for elliptic curve 8470ba3

-4	-3	5	-7	-11
67760cg3	76230y3	42350u3	59290cv3	770e4

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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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