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
deg	192	Modular degree for the optimal curve
Δ	110160 = 24 · 34 · 5 · 17	Discriminant
Eigenvalues	2+ 3+ 5+  0  0 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-31,76]	[a1,a2,a3,a4,a6]
Generators	[-5:9:1]	Generators of the group modulo torsion
j	212629504/6885	j-invariant
L	2.4837450423787	L(r)(E,1)/r!
Ω	3.31878966046	Real period
R	0.74838880932105	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	4080k1 16320bf1 6120w1 10200bi1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040a1

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 2040a1

-4	8	-3	5	-7	17
4080k1	16320bf1	6120w1	10200bi1	99960bs1	34680x1

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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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