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	16800bq	Isogeny class
Conductor	16800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-225792000 = -1 · 212 · 32 · 53 · 72	Discriminant
Eigenvalues	2- 3+ 5- 7- -6 -6  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-113,897]	[a1,a2,a3,a4,a6]
Generators	[-8:35:1] [-7:36:1]	Generators of the group modulo torsion
j	-314432/441	j-invariant
L	6.0657824593481	L(r)(E,1)/r!
Ω	1.592001486882	Real period
R	0.47627016285234	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16800bb2 33600ea1 50400cb2 16800bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16800bq2

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

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Quadratic twists for elliptic curve 16800bq2

-4	8	-3	5	-7
16800bb2	33600ea1	50400cb2	16800bc2	117600ih2

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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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