Cremona's table of elliptic curves

2870 = 2 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 41-	Signs for the Atkin-Lehner involutions
Class	2870d	Isogeny class
Conductor	2870	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-1489101042232384000 = -1 · 29 · 53 · 712 · 412	Discriminant
Eigenvalues	2+ -2 5+ 7-  0  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,240841,37133082]	[a1,a2,a3,a4,a6]
Generators	[360:12878:1]	Generators of the group modulo torsion
j	1544961173514772856471/1489101042232384000	j-invariant
L	1.6539828014048	L(r)(E,1)/r!
Ω	0.17641463536303	Real period
R	1.562590312685	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22960j4 91840v4 25830bi4 14350p4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870d4

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

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Quadratic twists for elliptic curve 2870d4

-4	8	-3	5	-7	41
22960j4	91840v4	25830bi4	14350p4	20090c4	117670a4

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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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