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	4040b	Isogeny class
Conductor	4040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2585600 = 210 · 52 · 101	Discriminant
Eigenvalues	2+  0 5-  4  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-53867,-4812074]	[a1,a2,a3,a4,a6]
Generators	[29665574:611234295:54872]	Generators of the group modulo torsion
j	16880764960659204/2525	j-invariant
L	4.069097326473	L(r)(E,1)/r!
Ω	0.31337825461364	Real period
R	12.984619278991	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	8080b3 32320a4 36360q4 20200g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4040b3

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

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Quadratic twists for elliptic curve 4040b3

-4	8	-3	5
8080b3	32320a4	36360q4	20200g3

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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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