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	8	Product of Tamagawa factors cp
Δ	63000000000 = 29 · 32 · 59 · 7	Discriminant
Eigenvalues	2- 3- 5+ 7-  4  2  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2100008,-1172031012]	[a1,a2,a3,a4,a6]
j	128025588102048008/7875	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	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16800f3 33600bc4 50400br4 3360f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800by2

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 16800by2

-4	8	-3	5	-7
16800f3	33600bc4	50400br4	3360f2	117600fd4

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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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