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	16800bh	Isogeny class
Conductor	16800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	2953125000000 = 26 · 33 · 512 · 7	Discriminant
Eigenvalues	2- 3+ 5+ 7-  2  4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-5258,123012]	[a1,a2,a3,a4,a6]
Generators	[-53:500:1]	Generators of the group modulo torsion
j	16079333824/2953125	j-invariant
L	4.6715954308924	L(r)(E,1)/r!
Ω	0.76319808734132	Real period
R	3.060539267837	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	16800bs1 33600go2 50400bl1 3360l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800bh1

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

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Quadratic twists for elliptic curve 16800bh1

-4	8	-3	5	-7
16800bs1	33600go2	50400bl1	3360l1	117600gt1

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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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