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	8470h	Isogeny class
Conductor	8470	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	5120	Modular degree for the optimal curve
Δ	-4960370800 = -1 · 24 · 52 · 7 · 116	Discriminant
Eigenvalues	2+  0 5+ 7- 11-  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,280,2800]	[a1,a2,a3,a4,a6]
Generators	[3:59:1]	Generators of the group modulo torsion
j	1367631/2800	j-invariant
L	2.9872064581579	L(r)(E,1)/r!
Ω	0.94516010312538	Real period
R	0.79013239351727	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	67760ba1 76230fe1 42350bu1 59290br1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470h1

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

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Quadratic twists for elliptic curve 8470h1

-4	-3	5	-7	-11
67760ba1	76230fe1	42350bu1	59290br1	70a1

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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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