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	5040bk	Isogeny class
Conductor	5040	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-128024064000 = -1 · 212 · 36 · 53 · 73	Discriminant
Eigenvalues	2- 3- 5- 7+ -3  5 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,1248,-2896]	[a1,a2,a3,a4,a6]
j	71991296/42875	j-invariant
L	1.8262169690893	L(r)(E,1)/r!
Ω	0.60873898969643	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	315a2 20160du2 560c2 25200eq2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bk2

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	5	-3	-2	-6	-3	4	2	12	10	9	-12	0	8	4	0	2	1	12	12	-1

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Quadratic twists for elliptic curve 5040bk2

-4	8	-3	5	-7
315a2	20160du2	560c2	25200eq2	35280ek2

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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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