Cremona's table of elliptic curves

16800 = 2⁵ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	16800f	Isogeny class
Conductor	16800	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	123046875000000000 = 29 · 32 · 518 · 7	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-147008,13681512]	[a1,a2,a3,a4,a6]
Generators	[61:2222:1]	Generators of the group modulo torsion
j	43919722445768/15380859375	j-invariant
L	3.5859393743391	L(r)(E,1)/r!
Ω	0.30358991230296	Real period
R	5.9058934915477	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	16800by3 33600cl3 50400de3 3360z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800f2

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
+	+	+	+	-4	2	2	-8	0	-2	0	6	2	4	8	6	0	-2	4	-4	2	-4	-12	18	-6

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Quadratic twists for elliptic curve 16800f2

-4	8	-3	5	-7
16800by3	33600cl3	50400de3	3360z2	117600dg3

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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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