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	5040bi	Isogeny class
Conductor	5040	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-2773897917235200 = -1 · 228 · 310 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,30237,1524962]	[a1,a2,a3,a4,a6]
j	1023887723039/928972800	j-invariant
L	1.1846453990106	L(r)(E,1)/r!
Ω	0.29616134975265	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	630c1 20160ff1 1680p1 25200dz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bi1

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	-2	-2	-4	-8	2	0	6	6	4	0	10	12	14	12	-8	10	-16	-12	-10	2

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Quadratic twists for elliptic curve 5040bi1

-4	8	-3	5	-7
630c1	20160ff1	1680p1	25200dz1	35280fs1

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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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