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	5040x	Isogeny class
Conductor	5040	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	-7.2875511985825E+19	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4  6 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-461403,428072202]	[a1,a2,a3,a4,a6]
Generators	[-611:21952:1]	Generators of the group modulo torsion
j	-134745327251163/903920796800	j-invariant
L	3.6528721591884	L(r)(E,1)/r!
Ω	0.16721746587595	Real period
R	0.54612598929981	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	630g2 20160dm2 5040bb2 25200ct2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040x2

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
-	+	+	-	-4	6	-4	-6	0	6	4	8	-10	2	10	-14	-4	-8	-6	-2	-10	-16	-8	-2	2

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Quadratic twists for elliptic curve 5040x2

-4	8	-3	5	-7
630g2	20160dm2	5040bb2	25200ct2	35280dp2

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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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