Cremona's table of elliptic curves

16704 = 2⁶ · 3² · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 29-	Signs for the Atkin-Lehner involutions
Class	16704ca	Isogeny class
Conductor	16704	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-251683766009856 = -1 · 219 · 39 · 293	Discriminant
Eigenvalues	2- 3+ -3  1  0 -2 -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3564,-767664]	[a1,a2,a3,a4,a6]
Generators	[858:25056:1]	Generators of the group modulo torsion
j	-970299/48778	j-invariant
L	3.9485041936395	L(r)(E,1)/r!
Ω	0.24292293268682	Real period
R	0.67725597681803	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16704l2 4176p2 16704br1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 16704ca2

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
-	+	-3	1	0	-2	-3	5	6	-	4	-11	-3	-1	3	-6	-9	-2	8	6	8	16	-12	-6	-4

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Quadratic twists for elliptic curve 16704ca2

-4	8	-3
16704l2	4176p2	16704br1

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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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