Cremona's table of elliptic curves

16820 = 2² · 5 · 29²

Field	Data	Notes
Atkin-Lehner	2- 5- 29+	Signs for the Atkin-Lehner involutions
Class	16820c	Isogeny class
Conductor	16820	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	60480	Modular degree for the optimal curve
Δ	1000492825922000 = 24 · 53 · 298	Discriminant
Eigenvalues	2-  0 5- -2  4 -6  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-26912,-756059]	[a1,a2,a3,a4,a6]
Generators	[-33:310:1]	Generators of the group modulo torsion
j	226492416/105125	j-invariant
L	4.6620299582969	L(r)(E,1)/r!
Ω	0.38975998147638	Real period
R	3.9870947761556	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	67280w1 84100b1 580b1	Quadratic twists by: -4 5 29

Hecke Eigenvalues for elliptic curve 16820c1

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

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Quadratic twists for elliptic curve 16820c1

-4	5	29
67280w1	84100b1	580b1

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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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