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	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	47250000 = 24 · 33 · 56 · 7	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -4  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-132,-481]	[a1,a2,a3,a4,a6]
Generators	[-7:10:1]	Generators of the group modulo torsion
j	588791808/109375	j-invariant
L	3.9244722463434	L(r)(E,1)/r!
Ω	1.4265728063866	Real period
R	0.91699309673598	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	1260d1 20160cs1 5040v3 25200cz1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040z1

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 5040z1

-4	8	-3	5	-7
1260d1	20160cs1	5040v3	25200cz1	35280cw1

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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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