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	5040o	Isogeny class
Conductor	5040	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	-2100394800 = -1 · 24 · 37 · 52 · 74	Discriminant
Eigenvalues	2+ 3- 5- 7+  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,78,-2189]	[a1,a2,a3,a4,a6]
Generators	[27:140:1]	Generators of the group modulo torsion
j	4499456/180075	j-invariant
L	3.9181707293796	L(r)(E,1)/r!
Ω	0.70511115432274	Real period
R	2.7784064295104	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	2520t1 20160do1 1680e1 25200bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040o1

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

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Quadratic twists for elliptic curve 5040o1

-4	8	-3	5	-7
2520t1	20160do1	1680e1	25200bl1	35280z1

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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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