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	8470i	Isogeny class
Conductor	8470	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	19008	Modular degree for the optimal curve
Δ	-14705019236600 = -1 · 23 · 52 · 73 · 118	Discriminant
Eigenvalues	2+  1 5+ 7- 11- -1  6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4964,227962]	[a1,a2,a3,a4,a6]
Generators	[-74:474:1]	Generators of the group modulo torsion
j	-63088729/68600	j-invariant
L	3.5003986076283	L(r)(E,1)/r!
Ω	0.63741061671545	Real period
R	2.7457956581157	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	67760bc1 76230ew1 42350bw1 59290bv1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470i1

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
+	1	+	-	-	-1	6	-7	3	6	2	-4	0	-4	-6	0	-3	2	-4	0	-4	17	9	-18	-10

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Quadratic twists for elliptic curve 8470i1

-4	-3	5	-7	-11
67760bc1	76230ew1	42350bw1	59290bv1	8470r1

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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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