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	5040y	Isogeny class
Conductor	5040	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	6193152000 = 218 · 33 · 53 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+  0  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-747,-6886]	[a1,a2,a3,a4,a6]
Generators	[-17:30:1]	Generators of the group modulo torsion
j	416832723/56000	j-invariant
L	4.0131730255527	L(r)(E,1)/r!
Ω	0.92132502679977	Real period
R	0.72597851080715	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	630h1 20160cr1 5040u3 25200cx1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040y1

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	0	-2	0	-6	-8	-4	-6	-2	-6	-6	12	8	-2	6	2	16	0	-6	-10

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Quadratic twists for elliptic curve 5040y1

-4	8	-3	5	-7
630h1	20160cr1	5040u3	25200cx1	35280cv1

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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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