Cremona's table of elliptic curves

870 = 2 · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	870i	Isogeny class
Conductor	870	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3692006820 = 22 · 32 · 5 · 295	Discriminant
Eigenvalues	2- 3- 5- -2  2  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2136580,-1202240020]	[a1,a2,a3,a4,a6]
j	1078651622544688278688321/3692006820	j-invariant
L	3.1218337583442	L(r)(E,1)/r!
Ω	0.12487335033377	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	25	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6960x3 27840o3 2610e3 4350a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870i3

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

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Quadratic twists for elliptic curve 870i3

-4	8	-3	5	-7	-11	29
6960x3	27840o3	2610e3	4350a3	42630ce3	105270bc3	25230e3

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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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