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	2040a	Isogeny class
Conductor	2040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	32640000 = 210 · 3 · 54 · 17	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1096,-13604]	[a1,a2,a3,a4,a6]
Generators	[81:650:1]	Generators of the group modulo torsion
j	142315306276/31875	j-invariant
L	2.4837450423787	L(r)(E,1)/r!
Ω	0.82969741511501	Real period
R	2.9935552372842	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	4080k3 16320bf3 6120w3 10200bi3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040a3

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

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Quadratic twists for elliptic curve 2040a3

-4	8	-3	5	-7	17
4080k3	16320bf3	6120w3	10200bi3	99960bs4	34680x4

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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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