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	16800b	Isogeny class
Conductor	16800	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	-147000000 = -1 · 26 · 3 · 56 · 72	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  2  2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,42,-588]	[a1,a2,a3,a4,a6]
Generators	[8:14:1]	Generators of the group modulo torsion
j	8000/147	j-invariant
L	4.104462340497	L(r)(E,1)/r!
Ω	0.8920849104971	Real period
R	2.3004886038313	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	16800bw1 33600ch2 50400db1 672g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800b1

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	2	-4	4	-6	-2	0	6	8	-8	-4	6	0	-14	4	2	2	-4	12	0	-6

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Quadratic twists for elliptic curve 16800b1

-4	8	-3	5	-7
16800bw1	33600ch2	50400db1	672g1	117600cw1

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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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