Cremona's table of elliptic curves

1166 = 2 · 11 · 53

Field	Data	Notes
Atkin-Lehner	2+ 11+ 53-	Signs for the Atkin-Lehner involutions
Class	1166b	Isogeny class
Conductor	1166	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3103892 = 22 · 114 · 53	Discriminant
Eigenvalues	2+  0 -2  0 11+  6 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1133,-14399]	[a1,a2,a3,a4,a6]
j	160927045436457/3103892	j-invariant
L	0.82285746505662	L(r)(E,1)/r!
Ω	0.82285746505662	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	9328m4 37312l4 10494e4 29150k4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1166b3

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

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Quadratic twists for elliptic curve 1166b3

-4	8	-3	5	-7	-11	53
9328m4	37312l4	10494e4	29150k4	57134f4	12826i4	61798e4

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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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