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	5040k	Isogeny class
Conductor	5040	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-725896442880 = -1 · 210 · 310 · 5 · 74	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-363,-41078]	[a1,a2,a3,a4,a6]
Generators	[59:378:1]	Generators of the group modulo torsion
j	-7086244/972405	j-invariant
L	3.7517086849848	L(r)(E,1)/r!
Ω	0.40064596147981	Real period
R	1.1705186890964	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	2520o4 20160fb4 1680i4 25200v3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040k4

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	-2	0	0	-6	-4	-2	-10	-4	0	-2	4	6	12	12	-2	0	4	-10	-2

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Quadratic twists for elliptic curve 5040k4

-4	8	-3	5	-7
2520o4	20160fb4	1680i4	25200v3	35280cf3

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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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