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	2040d	Isogeny class
Conductor	2040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-4080 = -1 · 24 · 3 · 5 · 17	Discriminant
Eigenvalues	2+ 3+ 5- -3 -3  4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,0,-3]	[a1,a2,a3,a4,a6]
Generators	[2:1:1]	Generators of the group modulo torsion
j	-256/255	j-invariant
L	2.5863163748034	L(r)(E,1)/r!
Ω	1.9816218273195	Real period
R	0.65257566785633	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4080p1 16320bd1 6120t1 10200bh1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040d1

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
+	+	-	-3	-3	4	-	-1	4	1	-4	-3	-3	-4	-9	-9	6	-8	2	0	3	-10	0	-14	2

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Quadratic twists for elliptic curve 2040d1

-4	8	-3	5	-7	17
4080p1	16320bd1	6120t1	10200bh1	99960bi1	34680s1

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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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