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	5040m	Isogeny class
Conductor	5040	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2048	Modular degree for the optimal curve
Δ	6123600 = 24 · 37 · 52 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7- -4 -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1578,24127]	[a1,a2,a3,a4,a6]
Generators	[11:90:1]	Generators of the group modulo torsion
j	37256083456/525	j-invariant
L	3.5497863744107	L(r)(E,1)/r!
Ω	2.1793943174741	Real period
R	0.81439745574011	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	2520e1 20160fg1 1680j1 25200be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040m1

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	-2	-2	4	0	10	0	6	6	4	-8	-6	-4	-10	-4	-16	-14	-8	-4	-10	10

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Quadratic twists for elliptic curve 5040m1

-4	8	-3	5	-7
2520e1	20160fg1	1680j1	25200be1	35280cq1

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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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