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	19757502464000000 = 218 · 56 · 76 · 41	Discriminant
Eigenvalues	2+ -2 5+ 7-  0  2  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-79159,5261082]	[a1,a2,a3,a4,a6]
Generators	[-54:3089:1]	Generators of the group modulo torsion
j	54855063622783623529/19757502464000000	j-invariant
L	1.6539828014048	L(r)(E,1)/r!
Ω	0.35282927072606	Real period
R	0.78129515634252	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	22960j3 91840v3 25830bi3 14350p3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2870d3

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 2870d3

-4	8	-3	5	-7	41
22960j3	91840v3	25830bi3	14350p3	20090c3	117670a3

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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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