Cremona's table of elliptic curves

4040 = 2³ · 5 · 101

Field	Data	Notes
Atkin-Lehner	2- 5- 101-	Signs for the Atkin-Lehner involutions
Class	4040d	Isogeny class
Conductor	4040	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	40400 = 24 · 52 · 101	Discriminant
Eigenvalues	2-  2 5-  2  0  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-35,92]	[a1,a2,a3,a4,a6]
j	304900096/2525	j-invariant
L	3.6467164268845	L(r)(E,1)/r!
Ω	3.6467164268845	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	8080c1 32320b1 36360b1 20200c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4040d1

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	0	2	2	-4	4	-6	8	10	-2	4	8	0	0	10	6	-8	8	-16	6	6	2

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Quadratic twists for elliptic curve 4040d1

-4	8	-3	5
8080c1	32320b1	36360b1	20200c1

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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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