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	2057529600 = 28 · 38 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1263,-17138]	[a1,a2,a3,a4,a6]
Generators	[62:378:1]	Generators of the group modulo torsion
j	1193895376/11025	j-invariant
L	3.7517086849848	L(r)(E,1)/r!
Ω	0.80129192295963	Real period
R	2.3410373781927	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2520o2 20160fb2 1680i2 25200v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040k2

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 5040k2

-4	8	-3	5	-7
2520o2	20160fb2	1680i2	25200v2	35280cf2

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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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