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	16	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	631250000 = 24 · 58 · 101	Discriminant
Eigenvalues	2+  0 5-  4  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-242,-799]	[a1,a2,a3,a4,a6]
Generators	[517:11750:1]	Generators of the group modulo torsion
j	97960237056/39453125	j-invariant
L	4.069097326473	L(r)(E,1)/r!
Ω	1.2535130184546	Real period
R	3.2461548197479	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8080b1 32320a1 36360q1 20200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4040b1

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 4040b1

-4	8	-3	5
8080b1	32320a1	36360q1	20200g1

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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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