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	16800br	Isogeny class
Conductor	16800	Conductor
∏ cp	384	Product of Tamagawa factors cp
Δ	-8332994880000000 = -1 · 212 · 312 · 57 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,8367,4384863]	[a1,a2,a3,a4,a6]
Generators	[-102:1575:1]	Generators of the group modulo torsion
j	1012048064/130203045	j-invariant
L	5.7951304303555	L(r)(E,1)/r!
Ω	0.31820995300587	Real period
R	0.75881903017353	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	16800g4 33600a1 50400s2 3360g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800br4

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

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Quadratic twists for elliptic curve 16800br4

-4	8	-3	5	-7
16800g4	33600a1	50400s2	3360g4	117600ek2

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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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