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	96	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	43758225000000 = 26 · 36 · 58 · 74	Discriminant
Eigenvalues	2- 3- 5+ 7+  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-22258,1230488]	[a1,a2,a3,a4,a6]
Generators	[-52:1500:1]	Generators of the group modulo torsion
j	1219555693504/43758225	j-invariant
L	5.7951304303555	L(r)(E,1)/r!
Ω	0.63641990601174	Real period
R	1.5176380603471	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	16800g1 33600a2 50400s1 3360g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800br1

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 16800br1

-4	8	-3	5	-7
16800g1	33600a2	50400s1	3360g1	117600ek1

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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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