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	5040bl	Isogeny class
Conductor	5040	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	187535250000 = 24 · 37 · 56 · 73	Discriminant
Eigenvalues	2- 3- 5- 7+  6 -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2712,-50209]	[a1,a2,a3,a4,a6]
j	189123395584/16078125	j-invariant
L	1.9954623771995	L(r)(E,1)/r!
Ω	0.66515412573315	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1260j3 20160dy3 1680l3 25200et3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bl3

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
-	-	-	+	6	-4	-6	-2	0	-6	10	2	6	4	0	12	0	14	4	6	-4	16	-12	-6	-16

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Quadratic twists for elliptic curve 5040bl3

-4	8	-3	5	-7
1260j3	20160dy3	1680l3	25200et3	35280er3

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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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