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	51984ci	Isogeny class
Conductor	51984	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	518400	Modular degree for the optimal curve
Δ	-21352693685649408 = -1 · 215 · 36 · 197	Discriminant
Eigenvalues	2- 3-  0  1 -6 -5 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-806835,-279037838]	[a1,a2,a3,a4,a6]
j	-413493625/152	j-invariant
L	0.31858387556124	L(r)(E,1)/r!
Ω	0.079645968946289	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6498j1 5776l1 2736m1	Quadratic twists by: -4 -3 -19

Hecke Eigenvalues for elliptic curve 51984ci1

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	-6	-5	-3	-	3	9	-4	-2	0	-8	0	-3	-9	-10	5	6	-7	-10	-6	-12	10

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Quadratic twists for elliptic curve 51984ci1

-4	-3	-19
6498j1	5776l1	2736m1

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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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