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	870g	Isogeny class
Conductor	870	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-143224402500 = -1 · 22 · 34 · 54 · 294	Discriminant
Eigenvalues	2- 3+ 5-  4  0 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,1290,4215]	[a1,a2,a3,a4,a6]
j	237395127814559/143224402500	j-invariant
L	2.5341570608475	L(r)(E,1)/r!
Ω	0.63353926521187	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6960bo4 27840bl3 2610c4 4350n4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870g4

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

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Quadratic twists for elliptic curve 870g4

-4	8	-3	5	-7	-11	29
6960bo4	27840bl3	2610c4	4350n4	42630cz3	105270o3	25230k3

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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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