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	2040g	Isogeny class
Conductor	2040	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-6210454518000 = -1 · 24 · 37 · 53 · 175	Discriminant
Eigenvalues	2+ 3- 5+ -1 -5  4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,2104,114705]	[a1,a2,a3,a4,a6]
Generators	[184:2601:1]	Generators of the group modulo torsion
j	64347918907136/388153407375	j-invariant
L	3.264565196866	L(r)(E,1)/r!
Ω	0.54584320843079	Real period
R	0.085439637150723	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	4080e1 16320s1 6120v1 10200w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040g1

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
+	-	+	-1	-5	4	-	-1	-8	-1	0	-1	-5	-4	3	-5	-10	-4	6	0	1	-14	-8	2	-18

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Quadratic twists for elliptic curve 2040g1

-4	8	-3	5	-7	17
4080e1	16320s1	6120v1	10200w1	99960q1	34680f1

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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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