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	32	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	62015625000000 = 26 · 34 · 512 · 72	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-131258,18343512]	[a1,a2,a3,a4,a6]
Generators	[86:2772:1]	Generators of the group modulo torsion
j	250094631024064/62015625	j-invariant
L	3.5859393743391	L(r)(E,1)/r!
Ω	0.60717982460591	Real period
R	2.9529467457738	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	16800by1 33600cl2 50400de1 3360z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800f1

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 16800f1

-4	8	-3	5	-7
16800by1	33600cl2	50400de1	3360z1	117600dg1

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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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