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	257746484991098880 = 236 · 37 · 5 · 73	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-212043,-28562182]	[a1,a2,a3,a4,a6]
Generators	[-209:2574:1]	Generators of the group modulo torsion
j	353108405631241/86318776320	j-invariant
L	3.5435573885183	L(r)(E,1)/r!
Ω	0.22644891429684	Real period
R	3.9120935946211	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	630i3 20160en3 1680m3 25200eg3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bc3

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 5040bc3

-4	8	-3	5	-7
630i3	20160en3	1680m3	25200eg3	35280fe3

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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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