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
deg	320	Modular degree for the optimal curve
Δ	-4439040 = -1 · 210 · 3 · 5 · 172	Discriminant
Eigenvalues	2- 3- 5- -2  0  0 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40,128]	[a1,a2,a3,a4,a6]
j	-7086244/4335	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	4080g1 16320c1 6120h1 10200g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040o1

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 2040o1

-4	8	-3	5	-7	17
4080g1	16320c1	6120h1	10200g1	99960cg1	34680be1

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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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