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	2040b	Isogeny class
Conductor	2040	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8736	Modular degree for the optimal curve
Δ	-726152343750000 = -1 · 24 · 37 · 513 · 17	Discriminant
Eigenvalues	2+ 3+ 5+ -3  3  4 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,7644,-1273275]	[a1,a2,a3,a4,a6]
Generators	[86:113:1]	Generators of the group modulo torsion
j	3086803246205696/45384521484375	j-invariant
L	2.3818993836208	L(r)(E,1)/r!
Ω	0.24808116680762	Real period
R	4.8006453175622	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	4080m1 16320bk1 6120y1 10200bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2040b1

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	+	-5	0	-5	4	9	7	-8	-3	-7	6	-4	-14	-8	-9	2	-8	-6	-14

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Quadratic twists for elliptic curve 2040b1

-4	8	-3	5	-7	17
4080m1	16320bk1	6120y1	10200bj1	99960bv1	34680z1

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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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