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	8470v	Isogeny class
Conductor	8470	Conductor
∏ cp	168	Product of Tamagawa factors cp
deg	40320	Modular degree for the optimal curve
Δ	612748220170240 = 228 · 5 · 73 · 113	Discriminant
Eigenvalues	2-  0 5+ 7- 11+ -4  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-60468,5612951]	[a1,a2,a3,a4,a6]
Generators	[-27:2701:1]	Generators of the group modulo torsion
j	18370278334948779/460366807040	j-invariant
L	5.9166955476237	L(r)(E,1)/r!
Ω	0.51320868006952	Real period
R	0.27449594869628	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	67760w1 76230ce1 42350a1 59290dv1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470v1

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

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Quadratic twists for elliptic curve 8470v1

-4	-3	5	-7	-11
67760w1	76230ce1	42350a1	59290dv1	8470a1

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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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