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	5040bc	Isogeny class
Conductor	5040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	551124000000000000 = 214 · 39 · 512 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-627483,-187952182]	[a1,a2,a3,a4,a6]
Generators	[-457:1834:1]	Generators of the group modulo torsion
j	9150443179640281/184570312500	j-invariant
L	3.5435573885183	L(r)(E,1)/r!
Ω	0.16983668572263	Real period
R	5.2161247928282	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	630i4 20160en4 1680m4 25200eg5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bc4

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	6	-8	0	-6	4	-10	6	4	0	6	-12	-10	4	12	-10	-8	12	6	-10

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Quadratic twists for elliptic curve 5040bc4

-4	8	-3	5	-7
630i4	20160en4	1680m4	25200eg5	35280fe5

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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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