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	16800by	Isogeny class
Conductor	16800	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	-126023688000000000 = -1 · 212 · 38 · 59 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7-  4  2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-115633,-22859137]	[a1,a2,a3,a4,a6]
j	-2671731885376/1969120125	j-invariant
L	4.0132321107108	L(r)(E,1)/r!
Ω	0.12541350345971	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16800f4 33600bc1 50400br2 3360f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800by4

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 16800by4

-4	8	-3	5	-7
16800f4	33600bc1	50400br2	3360f4	117600fd2

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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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