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	51984ck	Isogeny class
Conductor	51984	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-2357455269888 = -1 · 212 · 313 · 192	Discriminant
Eigenvalues	2- 3-  0 -1 -2 -5  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-95475,11355122]	[a1,a2,a3,a4,a6]
Generators	[-287:3888:1] [137:920:1]	Generators of the group modulo torsion
j	-89289015625/2187	j-invariant
L	9.4344914279887	L(r)(E,1)/r!
Ω	0.75753307199668	Real period
R	0.77838940113216	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3249d2 17328s2 51984bx2	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984ck2

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	-1	-2	-5	4	-	-4	-8	-3	-3	-12	1	-6	4	-10	-13	11	-6	-11	1	0	-6	-2

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Quadratic twists for elliptic curve 51984ck2

-4	-3	-19
3249d2	17328s2	51984bx2

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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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