Cremona's table of elliptic curves

1640 = 2³ · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 5- 41-	Signs for the Atkin-Lehner involutions
Class	1640g	Isogeny class
Conductor	1640	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	419840 = 211 · 5 · 41	Discriminant
Eigenvalues	2-  0 5-  0  4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8747,-314874]	[a1,a2,a3,a4,a6]
j	36138584631042/205	j-invariant
L	1.9746710743451	L(r)(E,1)/r!
Ω	0.49366776858628	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3280f3 13120h3 14760d3 8200c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1640g3

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

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Quadratic twists for elliptic curve 1640g3

-4	8	-3	5	-7	41
3280f3	13120h3	14760d3	8200c3	80360l4	67240h4

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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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