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	2166b	Isogeny class
Conductor	2166	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4320	Modular degree for the optimal curve
Δ	1544610364992 = 26 · 33 · 197	Discriminant
Eigenvalues	2+ 3+  0 -4  0  4  6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2895,-5787]	[a1,a2,a3,a4,a6]
j	57066625/32832	j-invariant
L	0.70796486198683	L(r)(E,1)/r!
Ω	0.70796486198683	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	17328be1 69312bo1 6498v1 54150cr1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2166b1

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

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Quadratic twists for elliptic curve 2166b1

-4	8	-3	5	-7	-19
17328be1	69312bo1	6498v1	54150cr1	106134bc1	114a1

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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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