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	870d	Isogeny class
Conductor	870	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-371237651280 = -1 · 24 · 38 · 5 · 294	Discriminant
Eigenvalues	2+ 3- 5-  0  0 -2  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-993,-31772]	[a1,a2,a3,a4,a6]
j	-108129104595721/371237651280	j-invariant
L	1.5632095608566	L(r)(E,1)/r!
Ω	0.39080239021416	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	6960bc4 27840b3 2610j4 4350r4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870d4

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

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Quadratic twists for elliptic curve 870d4

-4	8	-3	5	-7	-11	29
6960bc4	27840b3	2610j4	4350r4	42630h3	105270cf3	25230s3

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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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