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	5040bc	Isogeny class
Conductor	5040	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	122903101440000 = 218 · 37 · 54 · 73	Discriminant
Eigenvalues	2- 3- 5+ 7+  0  2  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-50577483,-138447122182]	[a1,a2,a3,a4,a6]
Generators	[13973162749:-1734715931850:753571]	Generators of the group modulo torsion
j	4791901410190533590281/41160000	j-invariant
L	3.5435573885183	L(r)(E,1)/r!
Ω	0.05661222857421	Real period
R	15.648374378485	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	630i7 20160en7 1680m7 25200eg8	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 5040bc7

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

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Quadratic twists for elliptic curve 5040bc7

-4	8	-3	5	-7
630i7	20160en7	1680m7	25200eg8	35280fe8

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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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