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	2040o	Isogeny class
Conductor	2040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	7833600 = 211 · 32 · 52 · 17	Discriminant
Eigenvalues	2- 3- 5- -2  0  0 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-720,7200]	[a1,a2,a3,a4,a6]
j	20183398562/3825	j-invariant
L	2.2702565128649	L(r)(E,1)/r!
Ω	2.2702565128649	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4080g2 16320c2 6120h2 10200g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040o2

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

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Quadratic twists for elliptic curve 2040o2

-4	8	-3	5	-7	17
4080g2	16320c2	6120h2	10200g2	99960cg2	34680be2

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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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