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	2040c	Isogeny class
Conductor	2040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-4329728640000 = -1 · 210 · 34 · 54 · 174	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-680,100572]	[a1,a2,a3,a4,a6]
Generators	[-46:180:1]	Generators of the group modulo torsion
j	-34008619684/4228250625	j-invariant
L	2.7548786021808	L(r)(E,1)/r!
Ω	0.63724581349106	Real period
R	1.0807754809281	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	4080o4 16320z4 6120r4 10200bg4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040c4

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

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Quadratic twists for elliptic curve 2040c4

-4	8	-3	5	-7	17
4080o4	16320z4	6120r4	10200bg4	99960be3	34680p3

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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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