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	16800bt	Isogeny class
Conductor	16800	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	26040609000000000 = 29 · 312 · 59 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1639408,807355688]	[a1,a2,a3,a4,a6]
Generators	[-1282:28350:1]	Generators of the group modulo torsion
j	60910917333827912/3255076125	j-invariant
L	6.0959038096815	L(r)(E,1)/r!
Ω	0.355570583159	Real period
R	1.4286670725879	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16800bj2 33600ep4 50400bb4 3360e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800bt3

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	0	-4	2	-8	-10	2	4	4	-10	-4	-2	4	0	6	-8	-4	-6	-10

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Quadratic twists for elliptic curve 16800bt3

-4	8	-3	5	-7
16800bj2	33600ep4	50400bb4	3360e3	117600fb4

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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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