Cremona's table of elliptic curves

16884 = 2² · 3² · 7 · 67

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 67-	Signs for the Atkin-Lehner involutions
Class	16884k	Isogeny class
Conductor	16884	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	5514179328 = 28 · 38 · 72 · 67	Discriminant
Eigenvalues	2- 3-  2 7-  0  0 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3279,72182]	[a1,a2,a3,a4,a6]
Generators	[-29:378:1]	Generators of the group modulo torsion
j	20892021712/29547	j-invariant
L	5.9507233469102	L(r)(E,1)/r!
Ω	1.3524438628994	Real period
R	0.73332967947286	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	67536bj2 5628b2 118188bh2	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 16884k2

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	2	-2	0	-6	2	4	-12	-4	-4	4	-	6	6	-16	12	6	-8

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Quadratic twists for elliptic curve 16884k2

-4	-3	-7
67536bj2	5628b2	118188bh2

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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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