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	4040c	Isogeny class
Conductor	4040	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	20402000 = 24 · 53 · 1012	Discriminant
Eigenvalues	2+  2 5-  2 -4 -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-75,152]	[a1,a2,a3,a4,a6]
Generators	[-1:15:1]	Generators of the group modulo torsion
j	2955053056/1275125	j-invariant
L	5.080335925851	L(r)(E,1)/r!
Ω	1.9476148340713	Real period
R	0.8694970273342	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	8080d1 32320c1 36360o1 20200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4040c1

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

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Quadratic twists for elliptic curve 4040c1

-4	8	-3	5
8080d1	32320c1	36360o1	20200i1

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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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