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	870h	Isogeny class
Conductor	870	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	126150 = 2 · 3 · 52 · 292	Discriminant
Eigenvalues	2- 3- 5-  2 -2 -4  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-35,75]	[a1,a2,a3,a4,a6]
j	4750104241/126150	j-invariant
L	3.2900075814102	L(r)(E,1)/r!
Ω	3.2900075814102	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6960y2 27840k2 2610d2 4350b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870h2

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	6	4	0	+	-2	-10	0	-4	-8	10	0	-8	8	8	10	10	-6	8	-18

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Quadratic twists for elliptic curve 870h2

-4	8	-3	5	-7	-11	29
6960y2	27840k2	2610d2	4350b2	42630cf2	105270be2	25230d2

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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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