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	5040bn	Isogeny class
Conductor	5040	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-8360755200 = -1 · 216 · 36 · 52 · 7	Discriminant
Eigenvalues	2- 3- 5- 7-  4 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,333,-3726]	[a1,a2,a3,a4,a6]
Generators	[18:90:1]	Generators of the group modulo torsion
j	1367631/2800	j-invariant
L	4.2118632198786	L(r)(E,1)/r!
Ω	0.68144903221075	Real period
R	1.5451864412422	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	630e1 20160ei1 560d1 25200dy1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bn1

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	0	0	-6	-8	-10	-2	-4	8	2	-8	-14	12	-16	2	8	8	-10	2

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Quadratic twists for elliptic curve 5040bn1

-4	8	-3	5	-7
630e1	20160ei1	560d1	25200dy1	35280el1

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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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