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	5040z	Isogeny class
Conductor	5040	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	2700507600 = 24 · 39 · 52 · 73	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3132,67419]	[a1,a2,a3,a4,a6]
Generators	[13:170:1]	Generators of the group modulo torsion
j	10788913152/8575	j-invariant
L	3.9244722463434	L(r)(E,1)/r!
Ω	1.4265728063866	Real period
R	2.7509792902079	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	1260d3 20160cs3 5040v1 25200cz3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040z3

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

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Quadratic twists for elliptic curve 5040z3

-4	8	-3	5	-7
1260d3	20160cs3	5040v1	25200cz3	35280cw3

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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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