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	5040n	Isogeny class
Conductor	5040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-529079040000 = -1 · 211 · 310 · 54 · 7	Discriminant
Eigenvalues	2+ 3- 5- 7+  0  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2013,4034]	[a1,a2,a3,a4,a6]
Generators	[13:180:1]	Generators of the group modulo torsion
j	604223422/354375	j-invariant
L	3.9886126734322	L(r)(E,1)/r!
Ω	0.56151982300048	Real period
R	0.44395279005013	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	2520i4 20160dp4 1680a4 25200bm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040n4

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	-4	0	-2	-4	2	2	-8	-4	2	12	-14	-8	-8	-2	-8	-4	18	-2

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Quadratic twists for elliptic curve 5040n4

-4	8	-3	5	-7
2520i4	20160dp4	1680a4	25200bm3	35280bb3

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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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