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	128	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-240081946720000 = -1 · 28 · 54 · 7 · 118	Discriminant
Eigenvalues	2- -2 5- 7- 11-  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3930,-739100]	[a1,a2,a3,a4,a6]
Generators	[120:1150:1]	Generators of the group modulo torsion
j	3789119879/135520000	j-invariant
L	4.981436995637	L(r)(E,1)/r!
Ω	0.26761648029605	Real period
R	0.58169028283104	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	67760cb1 76230bb1 42350m1 59290df1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470bg1

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 8470bg1

-4	-3	5	-7	-11
67760cb1	76230bb1	42350m1	59290df1	770d1

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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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