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	5040be	Isogeny class
Conductor	5040	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-2699890341120 = -1 · 28 · 316 · 5 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+ -2  4 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4863,152602]	[a1,a2,a3,a4,a6]
Generators	[2:378:1]	Generators of the group modulo torsion
j	-68150496976/14467005	j-invariant
L	3.4881753406515	L(r)(E,1)/r!
Ω	0.77350973816399	Real period
R	2.2547714453673	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	1260f2 20160eq2 1680s2 25200ek2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040be2

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

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Quadratic twists for elliptic curve 5040be2

-4	8	-3	5	-7
1260f2	20160eq2	1680s2	25200ek2	35280fn2

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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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