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	16800ba	Isogeny class
Conductor	16800	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	677376000 = 212 · 33 · 53 · 72	Discriminant
Eigenvalues	2+ 3- 5- 7+ -4 -2  6  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-673,6383]	[a1,a2,a3,a4,a6]
Generators	[-1:84:1]	Generators of the group modulo torsion
j	65939264/1323	j-invariant
L	5.6495289666314	L(r)(E,1)/r!
Ω	1.6131488002074	Real period
R	0.2918478943121	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	16800bn2 33600bp1 50400ed2 16800bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800ba2

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	6	6	-2	-6	2	-8	12	4	-8	2	-12	-10	-4	-8	-2	8	0	-12	10

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Quadratic twists for elliptic curve 16800ba2

-4	8	-3	5	-7
16800bn2	33600bp1	50400ed2	16800bo2	117600by2

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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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