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	51984a	Isogeny class
Conductor	51984	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	656640	Modular degree for the optimal curve
Δ	-342310370648067072 = -1 · 210 · 39 · 198	Discriminant
Eigenvalues	2+ 3+  2 -3  6 -1  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-555579,161858682]	[a1,a2,a3,a4,a6]
Generators	[361:2888:1]	Generators of the group modulo torsion
j	-55404	j-invariant
L	7.1140198569684	L(r)(E,1)/r!
Ω	0.30402839395049	Real period
R	0.97496648319001	Regulator
r	1	Rank of the group of rational points
S	1.0000000000018	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25992a1 51984b1 51984e1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984a1

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	-3	6	-1	2	+	0	2	1	-7	0	1	0	4	-8	-11	-15	-6	9	13	14	-12	10

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Quadratic twists for elliptic curve 51984a1

-4	-3	-19
25992a1	51984b1	51984e1

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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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