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	8470bg	Isogeny class
Conductor	8470	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	5967946118750000 = 24 · 58 · 72 · 117	Discriminant
Eigenvalues	2- -2 5- 7- 11-  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-102550,-12089868]	[a1,a2,a3,a4,a6]
Generators	[-166:688:1]	Generators of the group modulo torsion
j	67324767141241/3368750000	j-invariant
L	4.981436995637	L(r)(E,1)/r!
Ω	0.26761648029605	Real period
R	0.29084514141552	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	67760cb2 76230bb2 42350m2 59290df2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470bg2

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	-	-	-	0	0	0	-4	-2	-2	-6	-8	12	-6	-6	-10	4	-8	-4	4	16	0	-6	14

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Quadratic twists for elliptic curve 8470bg2

-4	-3	5	-7	-11
67760cb2	76230bb2	42350m2	59290df2	770d2

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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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