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	96	Product of Tamagawa factors cp
Δ	1245197016000000000 = 212 · 33 · 59 · 78	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-530033,-138659937]	[a1,a2,a3,a4,a6]
Generators	[-497:1500:1]	Generators of the group modulo torsion
j	257307998572864/19456203375	j-invariant
L	6.0959038096815	L(r)(E,1)/r!
Ω	0.1777852915795	Real period
R	1.4286670725879	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	16800bj3 33600ep1 50400bb3 3360e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800bt2

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 16800bt2

-4	8	-3	5	-7
16800bj3	33600ep1	50400bb3	3360e2	117600fb3

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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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