Cremona's table of elliptic curves

51984 = 2⁴ · 3² · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 19-	Signs for the Atkin-Lehner involutions
Class	51984x	Isogeny class
Conductor	51984	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2.471480876079E+20	Discriminant
Eigenvalues	2+ 3- -2  0  0 -2 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4133811,-3145331630]	[a1,a2,a3,a4,a6]
Generators	[-251706:-2042425:216]	Generators of the group modulo torsion
j	111223479026/3518667	j-invariant
L	4.4758995249536	L(r)(E,1)/r!
Ω	0.10608483003663	Real period
R	10.547925474885	Regulator
r	1	Rank of the group of rational points
S	0.99999999999659	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25992k4 17328m3 2736j3	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984x4

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

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Quadratic twists for elliptic curve 51984x4

-4	-3	-19
25992k4	17328m3	2736j3

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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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