Cremona's table of elliptic curves

2166 = 2 · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3+ 19+	Signs for the Atkin-Lehner involutions
Class	2166f	Isogeny class
Conductor	2166	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2240	Modular degree for the optimal curve
Δ	3840162048 = 28 · 37 · 193	Discriminant
Eigenvalues	2- 3+  2  4 -2  4  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-967,-11587]	[a1,a2,a3,a4,a6]
j	14580432307/559872	j-invariant
L	3.4326254884727	L(r)(E,1)/r!
Ω	0.85815637211818	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17328bc1 69312bh1 6498g1 54150u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2166f1

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	4	-2	4	6	+	-2	-10	8	-8	-2	4	6	-10	-4	-14	8	0	10	-12	2	6	12

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Quadratic twists for elliptic curve 2166f1

-4	8	-3	5	-7	-19
17328bc1	69312bh1	6498g1	54150u1	106134cm1	2166c1

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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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