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	5040s	Isogeny class
Conductor	5040	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	166659897600 = 28 · 312 · 52 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7- -4 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1767,20774]	[a1,a2,a3,a4,a6]
j	3269383504/893025	j-invariant
L	1.9024399249841	L(r)(E,1)/r!
Ω	0.95121996249205	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2520h2 20160eg2 1680c2 25200bg2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040s2

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
+	-	-	-	-4	-6	2	8	4	-6	-4	-2	2	12	0	-2	-4	6	4	8	6	16	-4	18	6

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Quadratic twists for elliptic curve 5040s2

-4	8	-3	5	-7
2520h2	20160eg2	1680c2	25200bg2	35280bs2

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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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