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	2040i	Isogeny class
Conductor	2040	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-110976000 = -1 · 210 · 3 · 53 · 172	Discriminant
Eigenvalues	2+ 3- 5-  2  4  4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,80,-400]	[a1,a2,a3,a4,a6]
j	54607676/108375	j-invariant
L	2.9350903428949	L(r)(E,1)/r!
Ω	0.97836344763162	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	4080i1 16320g1 6120s1 10200x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040i1

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

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Quadratic twists for elliptic curve 2040i1

-4	8	-3	5	-7	17
4080i1	16320g1	6120s1	10200x1	99960f1	34680c1

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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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