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	32	Product of Tamagawa factors cp
Δ	16646400 = 28 · 32 · 52 · 172	Discriminant
Eigenvalues	2- 3- 5+  0 -4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-116,-480]	[a1,a2,a3,a4,a6]
Generators	[-6:6:1]	Generators of the group modulo torsion
j	680136784/65025	j-invariant
L	3.298735483821	L(r)(E,1)/r!
Ω	1.4626180856031	Real period
R	1.1276817633705	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	4080a2 16320l2 6120l2 10200e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040m2

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 2040m2

-4	8	-3	5	-7	17
4080a2	16320l2	6120l2	10200e2	99960cu2	34680bi2

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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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