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	63106084995030150 = 2 · 3 · 52 · 2910	Discriminant
Eigenvalues	2- 3- 5- -2  2  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2136610,-1202204578]	[a1,a2,a3,a4,a6]
j	1078697059648930939019041/63106084995030150	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	6960x4 27840o4 2610e4 4350a4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870i4

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 870i4

-4	8	-3	5	-7	-11	29
6960x4	27840o4	2610e4	4350a4	42630ce4	105270bc4	25230e4

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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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