Cremona's table of elliptic curves

5040 = 2⁴ · 3² · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	5040k	Isogeny class
Conductor	5040	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	78382080 = 210 · 37 · 5 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-20163,-1101998]	[a1,a2,a3,a4,a6]
Generators	[242:2862:1]	Generators of the group modulo torsion
j	1214399773444/105	j-invariant
L	3.7517086849848	L(r)(E,1)/r!
Ω	0.40064596147981	Real period
R	4.6820747563854	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	2520o3 20160fb3 1680i3 25200v4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040k3

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	2	-2	0	0	-6	-4	-2	-10	-4	0	-2	4	6	12	12	-2	0	4	-10	-2

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Quadratic twists for elliptic curve 5040k3

-4	8	-3	5	-7
2520o3	20160fb3	1680i3	25200v4	35280cf4

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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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