Cremona's table of elliptic curves

2040 = 2³ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	2040m	Isogeny class
Conductor	2040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1282882560 = 210 · 3 · 5 · 174	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-416,2640]	[a1,a2,a3,a4,a6]
Generators	[24:84:1]	Generators of the group modulo torsion
j	7793764996/1252815	j-invariant
L	3.298735483821	L(r)(E,1)/r!
Ω	1.4626180856031	Real period
R	2.255363526741	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	4080a3 16320l4 6120l3 10200e4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040m4

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	-2	+	4	0	-6	-4	2	-2	-4	-12	-6	4	-10	-4	8	6	4	-16	-6	14

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Quadratic twists for elliptic curve 2040m4

-4	8	-3	5	-7	17
4080a3	16320l4	6120l3	10200e4	99960cu3	34680bi3

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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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